Fractional Dynamic Calculus And Fractional Dynamic Equations On Time Scales

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Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Springer
ISBN 13 : 3319739549
Total Pages : 360 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales by : Svetlin G. Georgiev

Download or read book Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2018-04-12 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.

Dynamic Calculus and Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111182975
Total Pages : 336 pages
Book Rating : 4.1/5 (111 download)

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Book Synopsis Dynamic Calculus and Equations on Time Scales by : Svetlin G. Georgiev

Download or read book Dynamic Calculus and Equations on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-18 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest advancements in time scale calculus are the focus of this book. New types of time-scale integral transforms are discussed in the book, along with how they can be used to solve dynamic equations. Novel numerical techniques for partial dynamic equations on time scales are described. New time scale inequalities for exponentially convex functions are introduced as well.

Conformable Dynamic Equations on Time Scales

Author : Douglas R. Anderson
Publisher : CRC Press
ISBN 13 : 1000094111
Total Pages : 131 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Conformable Dynamic Equations on Time Scales by : Douglas R. Anderson

Download or read book Conformable Dynamic Equations on Time Scales written by Douglas R. Anderson and published by CRC Press. This book was released on 2020-08-29 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention in areas as diverse as mechanics, electronics, and anomalous diffusion. Conformable Dynamic Equations on Time Scales is devoted to the qualitative theory of conformable dynamic equations on time scales. This book summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book. Except for a few sections in Chapter 1, the results here are presented for the first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications. Features Can be used as a textbook at the graduate level as well as a reference book for several disciplines Suitable for an audience of specialists such as mathematicians, physicists, engineers, and biologists Contains a new definition of fractional derivative About the Authors Douglas R. Anderson is professor and chair of the mathematics department at Concordia College, Moorhead. His research areas of interest include dynamic equations on time scales and Ulam-type stability of difference and dynamic equations. He is also active in investigating the existence of solutions for boundary value problems. Svetlin G. Georgiev is currently professor at Sorbonne University, Paris, France and works in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, dynamic calculus on time scales, and integral equations.

Boundary Value Problems

Author : Svetlin Georgiev
Publisher :
ISBN 13 : 9783031382024
Total Pages : 0 pages
Book Rating : 4.3/5 (82 download)

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Book Synopsis Boundary Value Problems by : Svetlin Georgiev

Download or read book Boundary Value Problems written by Svetlin Georgiev and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. The author provides an introduction to each fractional dynamic equation before delving into the problems. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness of the solutions. In addition, this book: Explains the topic for a wide audience including physicists, engineers, biologists, and students of various disciplines Explores boundary value problems for advanced fractional dynamic equations on arbitrary time scales Presents a solution technique applicable to other problems for fractional dynamic equations on arbitrary time scales About the Author: Svetlin Georgiev, Ph.D., is an Assistant Professor in the Faculty of Mathematics and Informatics at Sofia University. He was previously affiliated with Sorbonne University. He is the author of several books, including Real Quaternion Calculus Handbook, Theory of Distributions, Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales, and Functional Dynamic Equations on Time Scales, published by Springer Nature. His current research interests include harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.

Boundary Value Problems

Author : Svetlin Georgiev
Publisher :
ISBN 13 : 9783031381980
Total Pages : 0 pages
Book Rating : 4.3/5 (819 download)

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Book Synopsis Boundary Value Problems by : Svetlin Georgiev

Advances on

Author : Svetlin Georgiev
Publisher :
ISBN 13 : 9789811275470
Total Pages : 0 pages
Book Rating : 4.2/5 (754 download)

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Book Synopsis Advances on by : Svetlin Georgiev

Download or read book Advances on written by Svetlin Georgiev and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format"--

Fractional Dynamics

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
ISBN 13 : 3642140033
Total Pages : 504 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Fractional Dynamics by : Vasily E. Tarasov

Download or read book Fractional Dynamics written by Vasily E. Tarasov and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

First Order Partial Dynamic Equations on Time Scales

Author : Svetlin G. Georgiev
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1036401952
Total Pages : 377 pages
Book Rating : 4.0/5 (364 download)

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Book Synopsis First Order Partial Dynamic Equations on Time Scales by : Svetlin G. Georgiev

Download or read book First Order Partial Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Cambridge Scholars Publishing. This book was released on 2024-03-05 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the theory of first order partial dynamic equations (PDEs) on time scales. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses, but students in mathematical and physical sciences will also find many sections relevant. This book contains five chapters, and each chapter consists of results with their proofs, numerous examples, and exercises with solutions. Each chapter concludes with a section featuring advanced practical problems with solutions followed by a section on notes and references, explaining its context within existing literature. The book presents a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques, and the text of this book is presented in a readable and mathematically solid format.

Fractional Dynamics

Author : Joseph Klafter
Publisher : World Scientific
ISBN 13 : 9814340596
Total Pages : 530 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Fractional Dynamics by : Joseph Klafter

Download or read book Fractional Dynamics written by Joseph Klafter and published by World Scientific. This book was released on 2012 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Springer Science & Business Media
ISBN 13 : 1461202019
Total Pages : 365 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

Advances On Fractional Dynamic Inequalities On Time Scales

Author : Svetlin G Georgiev
Publisher : World Scientific
ISBN 13 : 9811275483
Total Pages : 337 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Advances On Fractional Dynamic Inequalities On Time Scales by : Svetlin G Georgiev

Download or read book Advances On Fractional Dynamic Inequalities On Time Scales written by Svetlin G Georgiev and published by World Scientific. This book was released on 2023-08-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.

Advances in Dynamic Equations on Time Scales

Author : Martin Bohner
Publisher : Birkhauser
ISBN 13 :
Total Pages : 366 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advances in Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Advances in Dynamic Equations on Time Scales written by Martin Bohner and published by Birkhauser. This book was released on 2003 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.

Fractional Calculus View of Complexity

Author : Bruce J. West
Publisher : CRC Press
ISBN 13 : 149873801X
Total Pages : 303 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Fractional Calculus View of Complexity by : Bruce J. West

Download or read book Fractional Calculus View of Complexity written by Bruce J. West and published by CRC Press. This book was released on 2016-01-05 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 many

Recent Trends in Fractional Calculus and Its Applications

Author : Praveen Agarwal
Publisher : Elsevier
ISBN 13 : 0443185069
Total Pages : 302 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Recent Trends in Fractional Calculus and Its Applications by : Praveen Agarwal

Download or read book Recent Trends in Fractional Calculus and Its Applications written by Praveen Agarwal and published by Elsevier. This book was released on 2024-07-19 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics. The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences. Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences

Fractional Dynamics

Author : Vasilij E. Tarasov
Publisher :
ISBN 13 : 9787040294736
Total Pages : 504 pages
Book Rating : 4.2/5 (947 download)

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Book Synopsis Fractional Dynamics by : Vasilij E. Tarasov

Download or read book Fractional Dynamics written by Vasilij E. Tarasov and published by . This book was released on 2010 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Equations on Time Scales and Applications

Author : Ravi P Agarwal
Publisher : CRC Press
ISBN 13 : 1040103758
Total Pages : 599 pages
Book Rating : 4.0/5 (41 download)

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Book Synopsis Dynamic Equations on Time Scales and Applications by : Ravi P Agarwal

Download or read book Dynamic Equations on Time Scales and Applications written by Ravi P Agarwal and published by CRC Press. This book was released on 2024-10-18 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. • Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales • Connects several new areas of dynamic equations on time scales with applications in different fields • Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales • Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena • Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics

Fractional Calculus

Author : Dumitru Baleanu
Publisher : World Scientific
ISBN 13 : 9813140054
Total Pages : 476 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Fractional Calculus by : Dumitru Baleanu

Download or read book Fractional Calculus written by Dumitru Baleanu and published by World Scientific. This book was released on 2016-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models. All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.