Mouffak Benchohra's Books

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

By: Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou

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Fractional Differential Equations And Inclusions: Classical And Advanced Topics

By: Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou

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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Page Count

326

Publisher

World Scientific

Published Date

ISBN 10

981126127X

ISBN 13

9789811261275

Advanced Topics in Fractional Differential Equations

A Fixed Point Approach

By: Mouffak Benchohra,Erdal Karapinar,Jamal Eddine Lazreg,Abdelkrim Salim

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Advanced Topics in Fractional Differential Equations

A Fixed Point Approach

By: Mouffak Benchohra,Erdal Karapinar,Jamal Eddine Lazreg,Abdelkrim Salim

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

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Page Count

190

Publisher

Springer Nature

Published Date

ISBN 10

3031269284

ISBN 13

9783031269288

Advanced Functional Evolution Equations and Inclusions

By: Saïd Abbas,Mouffak Benchohra

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Advanced Functional Evolution Equations and Inclusions

By: Saïd Abbas,Mouffak Benchohra

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

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Page Count

423

Publisher

Springer

Published Date

ISBN 10

3319177680

ISBN 13

9783319177687

Integro-Differential Equations

Analysis, Stability and Controllability

By: Mouffak Benchohra,Abdelkrim Salim,Yong Zhou

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Integro-Differential Equations

Analysis, Stability and Controllability

By: Mouffak Benchohra,Abdelkrim Salim,Yong Zhou

This book delves into semilinear evolution equations, impulsive differential equations, and integro-differential equations with different types of delay. The main objective is to investigate the existence of solutions and explore their approximate controllability, complete controllability, and attractivity. The study involves boundary conditions, nonlocal conditions, and impulsive conditions. The analysis presented in this book goes beyond traditional solutions and encompasses the study of solutions that are asymptotically almost automorphic and integro-differential equations with impulsive effects in both bounded and unbounded domains. The book also contains applications to nuclear physics, elementary particle physics, chemical engineering, and economics. This book is intended for researchers and professionals in the field of mathematics, physics and industrial engineering, as well as advanced graduate students.

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Page Count

296

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111437914

ISBN 13

9783111437910

Topics in Fractional Differential Equations

By: Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata

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Topics in Fractional Differential Equations

By: Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata

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.

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Page Count

403

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146144036X

ISBN 13

9781461440369

Fractional Difference, Differential Equations, and Inclusions

Analysis and Stability

By: Saïd Abbas,Bashir Ahmad,Mouffak Benchohra,Abdelkrim Salim

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Fractional Difference, Differential Equations, and Inclusions

Analysis and Stability

By: Saïd Abbas,Bashir Ahmad,Mouffak Benchohra,Abdelkrim Salim

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

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Page Count

400

Publisher

Elsevier

Published Date

ISBN 10

044323602X

ISBN 13

9780443236020

Topics in Fractional Differential Equations

By: Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata

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Topics in Fractional Differential Equations

By: Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata

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Page Count

403

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146144036X

ISBN 13

9781461440369

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

By: Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou

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Fractional Differential Equations And Inclusions: Classical And Advanced Topics

By: Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou

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Page Count

326

Publisher

World Scientific

Published Date

ISBN 10

981126127X

ISBN 13

9789811261275

Implicit Fractional Differential and Integral Equations

Existence and Stability

By: Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson

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Implicit Fractional Differential and Integral Equations

Existence and Stability

By: Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson

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

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Page Count

477

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

311055318X

ISBN 13

9783110553185

Integro-Differential Equations

Analysis, Stability and Controllability

By: Mouffak Benchohra,Abdelkrim Salim,Yong Zhou

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Integro-Differential Equations

Analysis, Stability and Controllability

By: Mouffak Benchohra,Abdelkrim Salim,Yong Zhou

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Solve jigsaw puzzle

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Page Count

296

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111437914

ISBN 13

9783111437910

Advanced Functional Evolution Equations and Inclusions

By: Saïd Abbas,Mouffak Benchohra

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Advanced Functional Evolution Equations and Inclusions

By: Saïd Abbas,Mouffak Benchohra

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Page Count

423

Publisher

Springer

Published Date

ISBN 10

3319177680

ISBN 13

9783319177687

Book's by Mouffak Benchohra

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Advanced Topics in Fractional Differential Equations

Advanced Topics in Fractional Differential Equations

Advanced Functional Evolution Equations and Inclusions

Advanced Functional Evolution Equations and Inclusions

Integro-Differential Equations

Integro-Differential Equations

Topics in Fractional Differential Equations

Topics in Fractional Differential Equations

Fractional Difference, Differential Equations, and Inclusions

Fractional Difference, Differential Equations, and Inclusions

Topics in Fractional Differential Equations

Topics in Fractional Differential Equations

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Implicit Fractional Differential and Integral Equations

Implicit Fractional Differential and Integral Equations

Integro-Differential Equations

Integro-Differential Equations

Advanced Functional Evolution Equations and Inclusions

Advanced Functional Evolution Equations and Inclusions

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