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Implicit Fractional Differential And Integral Equations

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Implicit Fractional Differential And Integral Equations

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Author : Saïd Abbas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05

Implicit Fractional Differential And Integral Equations written by Saïd Abbas 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 2018-02-05 with Mathematics categories.

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

Implicit Fractional Differential And Integral Equations

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Author : Saïd Abbas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05

Fractional Differential Equations And Inclusions Classical And Advanced Topics

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Author : Said Abbas
language : en
Publisher: World Scientific
Release Date : 2023-02-02

Fractional Differential Equations And Inclusions Classical And Advanced Topics written by Said Abbas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-02 with Mathematics categories.

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.

Fractional Difference Differential Equations And Inclusions

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Author : Saïd Abbas
language : en
Publisher: Elsevier
Release Date : 2024-01-11

Fractional Difference Differential Equations And Inclusions written by Saïd Abbas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-11 with Mathematics categories.

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

Fractional Differential Equations Inclusions And Inequalities With Applications

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Author : Sotiris K. Ntouyas
language : en
Publisher: MDPI
Release Date : 2020-11-09

Fractional Differential Equations Inclusions And Inequalities With Applications written by Sotiris K. Ntouyas and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-09 with Mathematics categories.

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 Differential Equations

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Author : Mouffak Benchohra
language : en
Publisher: Springer Nature
Release Date : 2023-07-10

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 2023-07-10 with Mathematics categories.

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.

Topics In Fractional Differential Equations

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Author : Saïd Abbas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-17

Topics In Fractional Differential Equations written by Saïd Abbas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-17 with Mathematics categories.

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.

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

Fixed Point Theory And Fractional Calculus

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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-05-10

Fixed Point Theory And Fractional Calculus written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.

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 fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

Positive Operators And Fixed Point Theorems With Applications

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Author : S. A. Mohiuddine
language : en
Publisher: Springer Nature
Release Date : 2025-05-29

Positive Operators And Fixed Point Theorems With Applications written by S. A. Mohiuddine and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-29 with Mathematics categories.

This book presents original research on the theory of positive operators, alongside fixed-point theorems and their diverse applications. It introduces various positive operators and explores their approximation properties, including Korovkin-type theorems, Voronovskaja-type results, convergence rate, and other related findings. Additionally, the book addresses the existence of solutions for various differential and integral equations in different Banach spaces by using Darbo-type fixed-point theorems. This book also presents an interplay between positive operators and fixed-point theory. Each chapter is self-contained, addressing a current problem and outlining solutions and potential applications. The chapters provide sufficient background to ensure that new definitions and results can be understood independently.

Implicit Fractional Differential And Integral Equations

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