Implicit Fractional Differential And Integral Equations

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Implicit Fractional Differential and Integral Equations

Author : Saïd Abbas
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311055318X
Total Pages : 477 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Implicit Fractional Differential and Integral Equations by : Saïd Abbas

Download or read book Implicit Fractional Differential and Integral Equations written by Saïd Abbas and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Topics in Fractional Differential Equations

Author : Saïd Abbas
Publisher : Springer Science & Business Media
ISBN 13 : 146144036X
Total Pages : 403 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Topics in Fractional Differential Equations by : Saïd Abbas

Download or read book Topics in Fractional Differential Equations written by Saïd Abbas and published by Springer Science & Business Media. This book was released on 2012-08-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists.

Implicit Fractional Differential and Integral Equations

Author : Saïd Abbas
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110553813
Total Pages : 362 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Implicit Fractional Differential and Integral Equations by : Saïd Abbas

Download or read book Implicit Fractional Differential and Integral Equations written by Saïd Abbas and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Advanced Topics in Fractional Differential Equations

Author : Mouffak Benchohra
Publisher : Springer Nature
ISBN 13 : 3031269284
Total Pages : 190 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Advanced Topics in Fractional Differential Equations by : Mouffak Benchohra

Download or read book Advanced Topics in Fractional Differential Equations written by Mouffak Benchohra and published by Springer Nature. This book was released on 2023-05-11 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Differential Equations And Inclusions: Classical And Advanced Topics

Author : Said Abbas
Publisher : World Scientific
ISBN 13 : 981126127X
Total Pages : 326 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Fractional Differential Equations And Inclusions: Classical And Advanced Topics by : Said Abbas

Download or read book Fractional Differential Equations And Inclusions: Classical And Advanced Topics written by Said Abbas and published by World Scientific. This book was released on 2023-02-02 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

The Analysis of Fractional Differential Equations

Author : Kai Diethelm
Publisher : Springer
ISBN 13 : 3642145744
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm

Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Fractional-Order Equations and Inclusions

Author : Michal Fečkan
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110521555
Total Pages : 506 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Fractional-Order Equations and Inclusions by : Michal Fečkan

Download or read book Fractional-Order Equations and Inclusions written by Michal Fečkan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-07 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Fractional Differential Equations

Author : Mouffak Benchohra
Publisher : Springer Nature
ISBN 13 : 303134877X
Total Pages : 197 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Fractional Differential Equations by : Mouffak Benchohra

Download or read book Fractional Differential Equations written by Mouffak Benchohra and published by Springer Nature. This book was released on 2023-07-10 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.

Numerical Methods for Fractional Differentiation

Author : Kolade M. Owolabi
Publisher : Springer Nature
ISBN 13 : 9811500983
Total Pages : 328 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Numerical Methods for Fractional Differentiation by : Kolade M. Owolabi

Download or read book Numerical Methods for Fractional Differentiation written by Kolade M. Owolabi and published by Springer Nature. This book was released on 2019-10-14 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 with exponential decay law, known as Caputo–Fabrizio differential and integral operators, those with power law, known as Riemann–Liouville fractional operators, and those for the generalized Mittag–Leffler function, known as the Atangana–Baleanu fractional operators. The book reviews existing numerical schemes associated with fractional operators including those with power law, while also highlighting new trends in numerical schemes for recently introduced differential and integral operators. In addition, the initial chapters address useful properties of each differential and integral fractional operator. Methods discussed in the book are subsequently used to solved problems arising in many fields of science, technology, and engineering, including epidemiology, chaos, solitons, fractals, diffusion, groundwater, and fluid mechanics. Given its scope, the book offers a valuable resource for graduate students of mathematics and engineering, and researchers in virtually all fields of science, technology, and engineering, as well as an excellent addition to libraries.

Fractional Difference, Differential Equations, and Inclusions

Author : Saïd Abbas
Publisher : Elsevier
ISBN 13 : 044323602X
Total Pages : 400 pages
Book Rating : 4.4/5 (432 download)

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Book Synopsis Fractional Difference, Differential Equations, and Inclusions by : Saïd Abbas

Download or read book Fractional Difference, Differential Equations, and Inclusions written by Saïd Abbas and published by Elsevier. This book was released on 2024-01-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of fractional calculus (FC) is more than 300 years old, and it presumably stemmed from a question about a fractional-order derivative raised in communication between L'Hopital and Leibniz in the year 1695. This branch of mathematical analysis is regarded as the generalization of classical calculus, as it deals with the derivative and integral operators of fractional order. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Some equations include delay effects of finite, infinite, or state-dependent nature. Others are subject to impulsive effect which may be fixed or non-instantaneous. The tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. All the abstract results are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences. Introduces notation, definitions, and foundational concepts of fractional q-calculus Presents existence and attractivity results for a class of implicit fractional q-difference equations in Banach and Fréchet spaces Focuses on the study of a class of coupled systems of Hilfer and Hilfer-Hadamard fractional differential equations

Ulam Type Stability

Author : Janusz Brzdęk
Publisher : Springer Nature
ISBN 13 : 3030289729
Total Pages : 514 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Ulam Type Stability by : Janusz Brzdęk

Download or read book Ulam Type Stability written by Janusz Brzdęk and published by Springer Nature. This book was released on 2019-10-29 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research results on Ulam type stability of various classes of linear and nonlinear operators; in particular on the stability of many functional equations in a single and several variables (also in the lattice environments, Orlicz spaces, quasi-b-Banach spaces, and 2-Banach spaces) and some orthogonality relations (e.g., of Birkhoff–James). A variety of approaches are presented, but a particular emphasis is given to that of fixed points, with some new fixed point results and their applications provided. Besides these several other topics are considered that are somehow related to the Ulam stability such as: invariant means, geometry of Banach function modules, queueing systems, semi-inner products and parapreseminorms, subdominant eigenvalue location of a bordered diagonal matrix and optimal forward contract design for inventory. New directions and several open problems regarding stability and non-stability concepts are included. Ideal for use as a reference or in a seminar, this book is aimed toward graduate students, scientists and engineers working in functional equations, difference equations, operator theory, functional analysis, approximation theory, optimization theory, and fixed point theory who wish to be introduced to a wide spectrum of relevant theories, methods and applications leading to interdisciplinary research. It advances the possibilities for future research through an extensive bibliography and a large spectrum of techniques, methods and applications.

Fractional Differential Equations

Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571668
Total Pages : 528 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Fractional Differential Equations by : Anatoly Kochubei

Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

Theory and Applications of Fractional Differential Equations

Author : A.A. Kilbas
Publisher : Elsevier
ISBN 13 : 9780444518323
Total Pages : 550 pages
Book Rating : 4.5/5 (183 download)

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Book Synopsis Theory and Applications of Fractional Differential Equations by : A.A. Kilbas

Download or read book Theory and Applications of Fractional Differential Equations written by A.A. Kilbas and published by Elsevier. This book was released on 2006-02-16 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.

Fractional Differential Equations, Inclusions and Inequalities with Applications

Author : Sotiris K. Ntouyas
Publisher : MDPI
ISBN 13 : 3039432184
Total Pages : 518 pages
Book Rating : 4.0/5 (394 download)

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Book Synopsis Fractional Differential Equations, Inclusions and Inequalities with Applications by : Sotiris K. Ntouyas

Download or read book Fractional Differential Equations, Inclusions and Inequalities with Applications written by Sotiris K. Ntouyas and published by MDPI. This book was released on 2020-11-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Fractional Integrals and Derivatives: “True” versus “False”

Author : Yuri Luchko
Publisher : MDPI
ISBN 13 : 303650494X
Total Pages : 280 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Fractional Integrals and Derivatives: “True” versus “False” by : Yuri Luchko

Download or read book Fractional Integrals and Derivatives: “True” versus “False” written by Yuri Luchko and published by MDPI. This book was released on 2021-03-16 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.

Time-Fractional Differential Equations

Author : Adam Kubica
Publisher : Springer Nature
ISBN 13 : 9811590664
Total Pages : 134 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Time-Fractional Differential Equations by : Adam Kubica

Download or read book Time-Fractional Differential Equations written by Adam Kubica and published by Springer Nature. This book was released on 2020-11-29 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs. To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.

Fractional Equations and Models

Author : Trifce Sandev
Publisher : Springer Nature
ISBN 13 : 3030296148
Total Pages : 357 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Fractional Equations and Models by : Trifce Sandev

Download or read book Fractional Equations and Models written by Trifce Sandev and published by Springer Nature. This book was released on 2019-11-23 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 demonstrate this using various examples of equations and models with fractional and generalized operators. Intended for students and researchers in mathematics, physics, chemistry, biology and engineering, it systematically offers a wealth of useful tools for fractional calculus.