Bantham Books, 2023. — 304 p. In recent years, special functions have been developed and applied in a variety of fields, such as combinatorics, astronomy, applied mathematics, physics, and engineering due to their remarkable properties. This volume expands our understanding of special functions by highlighting recent trends in numerical analysis. Interesting applications of...
New York: Springer, 2009. — 672 p. Fractional differentiation inequalities are by themselves an important area of research. They have many applications in pure and applied mathematics and many other applied sciences. One of the most important applications is in establishing the uniqueness of a solution in fractional differential equations and systems and in fractional partial...
Springer, 2021. — 501 p. — (Studies in Systems, Decision and Control 305). — ISBN: 978-3-030-56961-7. This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have...
Springer, 2018. — 322 p. — ISBN: 978-3-319-66936-6, 3319669362, 978-3-319-66935-9. This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read...
Cham: Springer, 2021. — 422 p. This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to...
CRC Press; Taylor & Francis Group, 2020. — 347 p. — ISBN: 978-0-367-51701-4. The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L'Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of...
Basel: MDPI, 2022. — 260 p. Among the numerous applications of the theory of fractional calculus in almost all applied sciences, applications in numerical analysis and various fields of physics and engineering stand out. Applications of inequalities involving function integrals and their derivatives, as well as applications of fractional differentiation inequalities, have...
Springer, 2012. — 337 pages. ISBN10: 364230897X This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive...
Walter de Gruyter, 2024. — 463 p. — (Series in Probability and Stochastics). — ISBN 9783110779813. Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering. This text addressed to researchers, graduate students, and practitioners combines deterministic fractional calculus with the analysis of the...
Walter de Gruyter, 2024. — 463 p. — (Series in Probability and Stochastics). — ISBN 9783110780222. Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering. This text addressed to researchers, graduate students, and practitioners combines deterministic fractional calculus with the analysis of the...
ISTE Ltd., John Wiley & Sons, Inc., 2014. XIII, 315 p. — ISBN: 978-1-84821-417-0. This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and...
ISTE, John Wiley & Sons, 2014. — 423 pages. — ISBN: 1848216793 ISBN13: 9781848216792 The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics....
World Scientific, 2017. — 474 p. The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and...
Berlin: de Gruyter, 2019. — 257 p. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine,...
Berlin: De Gruyter, 2019. — 292 p. This eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.
De Gruyter, 2019. — viii, 284 p. This eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.
Boca Raton: CRC Press, 2022. — 183 p. The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric...
Springer, 2021. — 314 p. — ISBN 978-3-030-69235-3. The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the...
Springer, 2021. — 314 p. — ISBN 978-3-030-69235-3. The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the...
Bentham Science Publishers, 2018. — 381 p. This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional...
Springer, 2022. — 381 p. — ISBN 13 9789811688010. Моделирование дробных производных в механике и технике This textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It...
N.Y.: Nova Science Pub Inc, 2014. — 244 p. Local Fractional Derivatives Fractional Variational Embedding and Lagrangian Formulations of Dissipative Partial Differential Equations A Class of Fractional Optimal Control Problems and Fractional Pontryagin's Systems. Variational Integrator and Existence of Continuous/Discrete Noether's Theorems Fractal Traps and Fractional Dynamics...
Basel: Springer, 2019. — 187 p. This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and...
Nova Science, 2015. — 294 p. The first volume of this two-volume book, presents history, the mathematical modeling and the applications of fractional order systems, and contains mathematical and theoretical studies and research related to this domain. This volume is made up of 11 chapters. The first chapter presents an analysis of the Caputo derivative and the pseudo state...
Springer, 2011. — 642 p. — 2nd ed. — ISBN: 3642205445, 9783642205446 When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary...
Cambridge Scholars Publishing, 2020. — 534 p. — ISBN 978-1-5275-4498-7. This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before...
Springer, 2019. — 329 p. — (Studies in Systems, Decision and Control, 240). — ISBN: 3030205231. This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional...
Springer, 2022. — 358 p. This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in...
Academic Press, 2017. — 109 p. — ISBN: 978-0-12-804248-9. This book presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of...
New York: Springer, 2019. — 339 p. This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks...
New York: Springer, 2016. - 556p. May be used for courses at the upper undergraduate level and above; the field is promoted by specialists Flexibility in its use, the text covers all aspects of discrete functional calculus Contains good examples, suitable problems, and comprehensive coverage of the topic This text provides the first comprehensive treatment of the discrete...
Springer, 2016. — 758 p. — ISBN10: 3319255606. — ISBN13: 978-3319255606 This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find...
2nd ed. — World Scientific Publishing Company, 2014. — 500 p. — ISBN: 9814551074, 9789814551076. The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are...
World Scientific Publishing, 2011. — 276 p. — ISBN: 9814340243. Fractional calculus is undergoing rapid and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student...
Cham: Springer, 2021. — 377 p. This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive...
BasleL MDPI, 2022. — 440 p. In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the...
Berlin/Boston: Walter de Gruyter, 2019. — 360 p. — ISBN: 978-3-11-057083-0. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional. Handbook of Fractional Calculus with Applications:...
CRC Press, 2023. — 432 p. — ISBN 978-1-032-41689-2. Численные методы для фрактально-дробных дифференциальных уравнений и инженерии: моделирование и моделирование This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators. The methods used, their convergence, stability, and error analysis are given, and this is the...
Berlin/Boston: Walter de Gruyter GmbH, 2019. — 489 p. — ISBN: 978-3-11-057162-2. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators,...
De Gruyter, 2019. — 519 p. — ISBN: 978-3110570823, 3110570823. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional c.
Springer, 2020. — 138 p. — (SpringerBriefs in Mathematics). — ISBN: 9811590656. This book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz....
Begel House Inc., 2006. — 704 p. This book is written for bioengineers who wish to learn more about fractional calculus (integration and differentiation of arbitrary order) and the ways in which it can be used to solve biomedical problems. The text covers a wide range of topics (bioelectrodes, biomaterials, neural networks, etc.) that will also be of interest to other...
Basel, Switzerland: MDPI, 2018. — 210 p. — ISBN: 3038972061. Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons). It can be considered a branch of mathematical physics that deals with integro-differential equations, where integrals are of convolution type and exhibit mainly singular kernels of...
Springer, 2015. — 142 p. — (Springer Briefs in Applied Sciences and Technology). — ISBN 978-3-319-14755-0. Передовые Методы в Мелком Исчислении Вариаций This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include...
Singapore: Springer, 2018. — 132 p. This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus....
New York: Pitman, 1979. - 190 p. This book is concerned with the study of certain spaces of generalized functions and their application to the theory of integral transforms defined on the positive real axis. Dr. McBride has purposely chosen to study only a few operators in considerable detail rather than hurriedly rushing over a larger number of transforms for which his results...
Singapore: Springer, 2022. — 212 p. The book investigates the fractional calculus-based approaches and their benefits to adopting in complex real-time areas. Another objective is to provide initial solutions for new areas where fractional theory has yet to verify the expertise. The book focuses on the latest scientific interest and illustrates the basic idea of general...
John Wiley & Sons , 1993. — 384 p. — ISBN: 0471588849
This study aims to make the solution of certain integral equations simpler to visualize. It presents material in a methodical manner and includes a bibliography covering references on the development of the subject from 1695 to modern times.
John Wiley @ Sons, 1993. — 376 p. — ISBN: 0471588849 Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its...
Elsevier Science, 2007. — 273 p. L-System Fractals covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals.Fractals generated from L-System including hybrid...
Arcler Press, 2024. — 354 p. "Basic Theory of Fractional Differential Equations" is a contemporary collection of 16 articles that explores modern methods and applications of FDEs. It covers the extended Jacobi elliptic function expansion method, numerical approximation techniques like -step continuous BDFs for FIVPs, stability theories, and various fractional derivatives. The...
Academic Press, 1974. — 248 p. — ISBN: 0125255500 Not only does this text explain the theory underlying the properties of the generalized operator, but it also illustrates the wide variety of fields to which these ideas may be applied. Topics include integer order, simple and complex functions, semiderivatives and semiintegrals, and transcendental functions. 1974 edition. This...
New York: Springer, 2011. — 159 p. — (Lecture Notes in Electrical Engineering 84).
In recent years fractional calculus has been rediscovered by scientists and engineers and applied in an increasing number of fields, such as electromagnetism, control engineering, and signal processing. The increase in the number of physical and engineering processes that are best described by...
World Scientific, 2016. — 395 p. — (Series in Computer Vision 4). — ISBN10: 9814725668. The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward...
Springer, 2019. — 338 p. — (Springer Series in Computational Mathematics 54). — ISBN: 9811500975. This book discusses numerical methods for solving partial differential and integral equations, as well as ordinary differential and integral equations, involving fractional differential and integral operators. Differential and integral operators presented in the book include those...
Berlin/Boston: de Gruyter, 2019. — 435 p. — ISBN: 978-3-11-057090-8. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This sixth volume collects authoritative chapters covering several applications of fractional calculus in control theory, including fractional controllers,...
Academic Press, 1998. - 340 pages. ISBN: 0125588402 (Mathematics in Science and Engineering, Volume 198)
This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word...
New York: Academic Press, 1998. — 366 p. This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is...
Boca Raton: CRC Press, Taylor & Francis Group, 2016. — XXXIV, 194 p. — ISBN13: 978-1-4987-2728-0 (eBook - PDF). Introduces Novel Applications for Solving Neutron Transport Equations. While deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical...
Chapman and Hall/CRC, 2024. — 565 p. Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how...
London: World Scientific, 2022. — 292 p. This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will...
Springer, 2019. — 345 p. Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical, chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory, as it might have once seemed. The present book seeks to...
New York: Ellis Horwood Ltd, 1989. — 408 p. We organized an International Symposium on Univalent Functions, Fractional Calculus, and Their Applications, which was held on May 1-5, 1988 at Koriyama Kenshu Kaikan under the auspices of the College of Engineering (Nihon University), Koriyama, Japan. The present volume contains invited addresses, papers, and talks presented (and/or...
Berlin: De Gruyter, 2020. — 397 p. Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for...
De Gruyter, 2019. — 316 p. — ISBN: 978-3-11-057088-5. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics. True PDF
De Gruyter, 2019. — 331 p. — ISBN: 978-3-11-057172-1. This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical...
Basel: MDPI, 2022. — 370 p. This book focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that...
Wiley-ISTE, 2019. — 307 p — ISBN: 978-1-119-64881-9. This book introduces an original fractional calculus methodology (‘the infinite state approach’) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer...
Wiley-ISTE, 2019. — 420 p. — ISBN: 978-1-119-68684-2. This book introduces an original fractional calculus methodology (the infinite state approach) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer...
New York: CRC Press, 2015. — 303 p.
This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about...
De Gruyter, 2017. — 238 p. — (Fractional Calculus in Applied Sciences and Engineering). — ISBN10: 3110534118, ISBN13: 978-3110534115. The book proposes complexity as source of allometry, which provides a new kind of force generated by the system's information gradient. Based on first principles, the scaling behavior of the probability density function is described by the exact...
CRC Press, 2024. — 164 p. — ISBN: 978-1-032-74293-9. This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this “new” calculus. This book is intended for those who are skeptical about...
Springer, 2024. — 412 p. — ISBN 9819920698. Fractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MatLAB toolboxes in fractional...
New York: Chapman & Hall/CRC, 2019. — 383 p. General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional...
Academic Press, 2020. — 447 p. — ISBN: 9780128172087. This book introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of...
Singapore: Bentham Science Publishers, 2022. — 275 p. In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been...
3rd edition. — Singapore: World Scientific, 2023. — 516 p. This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the...
NY, USA: Nova Science Publishers, Inc., 2014. — 306 p. — (Mathematics Research Developments). — ISBN: 978-1-63463-233-1. After presenting the first volume of this two-volume book, presenting a lot of mathematical and theoretical studies and research related to non-integer calculus, the second volume illustrates applications related to this domain. This volume is made up of 11...
New York: Springer, 2022. — 310 p. This book presents a concise and insightful view of the knowledge on fractional-order electrical circuits, which belongs to the subject of Electric Engineering and involves mathematics of fractional calculus. It offers an overview of fractional calculus and then describes and analyzes the basic theories and properties of fractional-order...
Учебно-методическое пособие. — Москва: МИСИ — МГСУ, 2023. — 69 с. Учебно-методическое пособие составлено в соответствии с программой дисциплины «Фрактальный анализ» и освещает методы, инструменты и сферы использования фрактального анализа в различных областях науки. В пособии представлены теоретические выкладки, примеры и практические задания по изучаемому курсу для закрепления...
Препринты ИПМ им. М.В. Келдыша. 2013. № 37. 26 с.
Работа посвящена локальным и нелокальным дифференциальным уравнениям тепло- и массопереноса в сплошных средах с памятью и в средах с фрактальной структурой. В работе исследованы краевые задачи для дифференциальных уравнений дробного порядка, а также методами теории возмущений исследованы несамосопряженные интегральные операторы,...
К.: НАН Украины, 2008. — 256 с. — ISBN 978-966-02-4384-2. Книга посвящена аппроксимационно-операционным методам моделирования динамических систем дробного и смешанного порядков. Рассмотрены методы аппроксимации сигналов обобщенными полиномами с различными системами базисных функций, построение на основе этих методов операционных исчислений неклассического типа и их применений к...
В работе рассмотрены вопросы применения аппарата дробных дифференциальных и интегральных операторов Римана — Лиувилля для анализа абсолютно непрерывных распределений. Показано, что в общем случае переход к дробным операторам существенно меняет привычные свойства плотностей, что делает неприменимыми некоторые стандартные методы статистического анализа. Выявлена неоднозначность...
Конспект лекций. — Самара: СГУ, 2009. — 121 с.
Дробные интегралы и дробные производные.
Обыкновенные дифференциальные уравнения дробного порядка, теоремы существования и единственности.
Методы точного решения дифференциальных уравнений дробного порядка.
Приложения теории дробного дифференцирования и и интегрирования в естественных науках.
Монография. — М.: Институт проблем управления (ИПУ) имени В.А. Трапезникова РАН, 2014. — 153 с. Данная работа содержит обзор по проблемам использования дробного интегро-дифференциального исчисления для описания различных систем и их динамики, в том числе с управлением. В первой части работы приведён исторический обзор развития дробного интегро-дифференциального исчисления и...
Учебно-методическое пособие для вузов. — Воронеж: Воронежский государственный университет (ВГУ), 2011. — 102 с. Учебно-методическое пособие по дисциплине «Основы дробного интегродифференциального исчисления и его применение к исследованию математических моделей» подготовлено на кафедре математического и прикладного анализа факультета прикладной математики, информатики и...
М.: Физматлит, 2003. — 272 с. — ISBN: 5-9221-0440-3. Монография посвящена основополагающим элементам дробного исчисления, качественно новым свойствам операторов дробного интегрирования и дифференцирования и их применению к решению проблем математического моделирования различных процессов и явлений в живых и неживых системах с фрактальной структурой и памятью; к локальным и...
Монография. — М.: Физматлит, 2003. — 272 с. — ISBN 5-9221-0440-3. Монография посвящена основополагающим элементам дробного исчисления, качественно новым свойствам операторов дробного интегрирования и дифференцирования и их применению к решению проблем математического моделирования различных процессов и явлений в живых и неживых системах с фрактальной структурой и памятью; к...
Хабаровск: Изд-во Тихоокеан. гос. ун-та, 2015. — 44 с. — ISBN: 978-5-7389-1632-8. Пособие разработано по материалам лекций для студентов факультета компьютерных и фундаментальных наук ТОГУ, прочитанных приглашённым лектором из Рима (Италия) профессором Энцо Орсингером. Изложено современное состояние дел в области, связанной с разнообразными способами введения понятий дробных...
Монография. — М.: Наука, 2005. — 199 с. Монография посвящена основополагающим элементам теории краевых задач для дифференциальных уравнений с частными производными дробного и континуального порядков. Впервые в отечественной литературе проведен анализ корректных постановок и рассмотрены методы решения и исследования основных краевых задач для широкого класса таких уравнений....
Монография. — М.: Наука, 2005. — 200 с. Монография посвящена основополагающим элементам теории краевых задач для дифференциальных уравнений с частными производными дробного и континуального порядков. Впервые в отечественной литературе проведен анализ корректных постановок и рассмотрены методы решения и исследования основных краевых задач для широкого класса таких уравнений....
Ростов на Дону: Ростовский университет, 1984. — 210 с. В монографии излагается теория гиперсингулярных интегралов, возникших при описании пространств функций многих переменных дробной гладкости, и даются приложения как к пространствам таких функций, так и к многомерным интегральным уравнениям первого рода. Гиперсингулярные интегралы являются операторами, обратными к операторам...
Монография. — Ростов на Дону: Ростовский государственный университет (РГУ), 1984. — 210 с. В монографии излагается теория гиперсингулярных интегралов, возникших при описании пространств функций многих переменных дробной гладкости, и даются приложения как к пространствам таких функций, так и к многомерным интегральным уравнениям первого рода. Гиперсингулярные интегралы являются...
Минск.: Наука и техника, 1987. — 688 с. Книга посвящена вопросам обобщения операций дифференцирования и интегрирования функций одной и многих переменных с целых порядков на дробные, действительные и комплексные, а также приложениям теории дробного интегрирования и дифференцирования к интегральным и дифференциальным уравнениям, теории функций. В ней впервые в мировой...
Минск: Наука и техника, 1987. — 688 с. Книга посвящена вопросам обобщения операций дифференцирования и интегрирования функций одной и многих переменных с целых порядков на дробные, действительные и комплексные, а также приложениям теории дробного интегрирования и дифференцирования к интегральным и дифференциальным уравнениям, теории функций. В ней впервые в мировой...
Ульяновск: Артишок, 2008. — 512 с. — ISBN 978-5-904198-01-5. Книга содержит изложение метода дробных производных и состоит из трех частей, раскрывающих физические основания метода, математический аппарат и примеры применения метода в различных областях физики: в механике и гидродинамике, вязкоупругости и термодинамике, физике диэлектриков и полупроводников, электротехнике и...
Ульяновск: Артишок, 2008. — 512 с. Книга содержит изложение метода дробных производных и состоит из трех частей, раскрывающих физические основания метода, математический аппарат и примеры применения метода в различных областях физики: в механике и гидродинамике, вязкоупругости и термодинамике, физике диэлектриков и полупроводников, электротехнике и физике плазмы, нанофизике и...
Учебное пособие. — Томск: Томский политехнический университет, 2010. — 118 с. В пособии последовательно изложены основы дробного анализа на основе вводимого дробного оператора, который обобщает операции дифференцирования и интегрирования степенных функций на случай вещественных порядков. Рассмотрены свойства дробного оператора. Предложена программа построения дробного анализа...
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