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Implicit Fractional Differential and Integral Equations

2018-02-05 Mathematics
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Release : 2018-02-05
Genre : Mathematics
Kind : eBook
Book Rating : 18X/5 ( reviews)

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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. This book was released on 2018-02-05. 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

2012-08-17 Mathematics
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Release : 2012-08-17
Genre : Mathematics
Kind : eBook
Book Rating : 36X/5 ( reviews)

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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. This book was released on 2012-08-17. 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

2018-02-05 Mathematics
Download Implicit Fractional Differential and Integral Equations PDF Online Free

Author :
Release : 2018-02-05
Genre : Mathematics
Kind : eBook
Book Rating : 813/5 ( reviews)

GET EBOOK


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. This book was released on 2018-02-05. 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

2023-05-11 Mathematics
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Release : 2023-05-11
Genre : Mathematics
Kind : eBook
Book Rating : 284/5 ( reviews)

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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. This book was released on 2023-05-11. 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

2023-02-02 Mathematics
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Release : 2023-02-02
Genre : Mathematics
Kind : eBook
Book Rating : 27X/5 ( reviews)

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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. This book was released on 2023-02-02. 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.

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