Solved Exercises In Fractional Calculus

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Solved Exercises In Fractional Calculus
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Author : Edmundo Capelas de Oliveira
language : en
Publisher: Springer
Release Date : 2019-05-31
Solved Exercises In Fractional Calculus written by Edmundo Capelas de Oliveira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Technology & Engineering categories.
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 derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.
Solved Exercises In Fractional Calculus
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Author : Edmundo Capelas de Oliveira
language : en
Publisher: Springer Nature
Release Date : 2025-04-28
Solved Exercises In Fractional Calculus written by Edmundo Capelas de Oliveira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-28 with Technology & Engineering categories.
This textbook provides a comprehensive exploration of special functions and fractional calculus, offering a structured approach through solved and proposed exercises. Covering key mathematical concepts such as Mittag-Leffler functions, Kilbas-Saigo functions, and the Erdélyi-Kober fractional integral, it balances theoretical insights with practical applications. Appendices introduce Barnes G-functions and demonstrate the use of Mathematica for fractional calculus, expanding the book’s accessibility. With an updated index and extensive references, this edition serves as a valuable resource for researchers, graduate students, and professionals in applied mathematics and related fields.
Fractional Differential Equations
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Author : Mouffak Benchohra
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-20
Fractional Differential Equations written by Mouffak Benchohra and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Technology & Engineering categories.
This book is devoted to the existence and uniqueness results for various classes of problems with periodic conditions. All of the problems in this book deal with fractional differential equations and some fractional derivatives such as the Riemann-Liouville, Caputo and Hilfer fractional derivatives. Classical fixed point theorems as well as the coincidence degree theory of Mawhin are employed as tools.
Fractional Differential Equations
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Author : Bangti Jin
language : en
Publisher: Springer Nature
Release Date : 2021-07-22
Fractional Differential Equations written by Bangti Jin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-22 with Mathematics categories.
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 bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.
An Introduction To Fractional Differential Equations
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Author : K. Balachandran
language : en
Publisher: Springer Nature
Release Date : 2023-11-23
An Introduction To Fractional Differential Equations written by K. Balachandran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-23 with Mathematics categories.
This is an introductory-level text on fractional calculus and fractional differential equations. Targeted to graduate students of mathematics and researchers, it contains several new definitions of fractional integrals and fractional derivatives. With interesting applications of the subject in several areas of physical sciences, life sciences, engineering, and technology, the book helps the students understand the importance and developments of this topic. The book is enriched with a list of useful references to published literature, and the presentation of the book is entirely new and easily comprehensible to the students. Some of the topics are refined, and new examples are included to supplement theories to help students understand the concepts easily and clearly.
Advanced Topics In Fractional Differential Equations
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Author : Mouffak Benchohra
language : en
Publisher: Springer Nature
Release Date : 2023-05-11
Advanced Topics In Fractional Differential Equations written by Mouffak Benchohra and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-11 with Mathematics categories.
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers’ understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors
Fractional Calculus An Introduction For Physicists Third Edition
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Author : Richard Herrmann
language : en
Publisher: World Scientific
Release Date : 2018-07-09
Fractional Calculus An Introduction For Physicists Third Edition written by Richard Herrmann and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Science categories.
'The third edition of this book is designed to carefully and coherently introduce fractional calculus to physicists, by applying the ideas to two distinct applications: classical problems and multi-particle quantum problems. There remain many open questions and the field remains an active area of research. Dr Herrmann’s book is an excellent introduction to this field of study.'Contemporary PhysicsThe book presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and contribute in the development of this exciting research area.This book is devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights.This new, extended edition includes additional chapters about numerical solution of the fractional Schrödinger equation, self-similarity and the geometric interpretation of non-isotropic fractional differential operators. Motivated by the positive response, new exercises with elaborated solutions are added, which significantly support a deeper understanding of the general aspects of the theory.Besides students as well as researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject.
Advances In Mathematical Modelling Applied Analysis And Computation
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Author : Jagdev Singh
language : en
Publisher: Springer Nature
Release Date : 2025-05-19
Advances In Mathematical Modelling Applied Analysis And Computation written by Jagdev Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-19 with Mathematics categories.
This book is a collection of research papers from the “7th International Conference on Mathematical Modelling, Applied Analysis and Computation” organized by Lebanese American University, Beirut, Lebanon from April 18–20, 2024. This proceeding contains research papers related with fundamental mathematical theory and methods in a very suitable manner and useful for handling various contemporary issues of physical, chemical and engineering sciences. The aim of this conference is to foster cooperation among mathematicians and scientists working in these areas. This book is a very useful resource for mathematicians, scientists and engineers working in the field of applied mathematics, analysis and computation for solving real life problems of different domains.
Computational Methods In The Fractional Calculus Of Variations
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Author : Ricardo Almeida
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-19
Computational Methods In The Fractional Calculus Of Variations written by Ricardo Almeida and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-19 with Mathematics categories.
This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.
Analytical Methods In Applied Mathematics
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Author : Edmundo Capelas de Oliveira
language : en
Publisher: Springer Nature
Release Date : 2024-11-14
Analytical Methods In Applied Mathematics written by Edmundo Capelas de Oliveira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-14 with Mathematics categories.
This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering. The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green's function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented. With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well.