Advanced Fractional Differential and Integral Equations

Said Abbas
University of Saida, Saida, Algeria

Mouffak Benchohra
University of Sidi Bel Abbes, King Abdulazziz University in Jeddah, Jeddah, Saudi Arabia

Gaston Mandata N’Guerekata
University Distinguished Professor of Mathematics, The World Academy of Sciences (TWAS) Research Professor, School of Computer, Mathematical and Natural Sciences, Morgan State University Baltimore, MD, USA

Series: Mathematics Research Developments
BISAC: MAT005000

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Fractional calculus deals with extensions of derivatives and integrals to non-integer orders. It represents a powerful tool in applied mathematics to study a myriad of problems from different fields of science and engineering, with many break-through results found in mathematical physics, finance, hydrology, biophysics, thermodynamics, control theory, statistical mechanics, astrophysics, cosmology and bioengineering. This book is devoted to the existence and uniqueness of solutions and some Ulam’s type stability concepts for various classes of functional differential and integral equations of fractional order.

Some equations present delay which may be finite, infinite or state-dependent. Others are subject to multiple time delay effect. The tools used include classical fixed point theorems. Other tools are based on the measure of non-compactness together with appropriates fixed point theorems. Each chapter concludes with a section devoted to notes and bibliographical remarks and all the presented results are illustrated by examples.

The content of the book is new and complements the existing literature in Fractional Calculus. It is useful for researchers and graduate students for research, seminars and advanced graduate courses, in pure and applied mathematics, engineering, biology and other applied sciences. (Imprint: Nova)

Preface

Introduction

Chapter 1 - Preliminary Background (pp. 1-20)

Chapter 2 - Nonlinear Differential Equations of Fractional Order (pp. 21-48)

Chapter 3 - Fractional Order Riemann-Liouville Integral Equations (pp. 49-70)

Chapter 4 - Fractional Order Riemann-Liouville Volterra-Stieltjes Quadratic Integral Equations (pp. 71-114)

Chapter 5 - Fractional Order Riemann-Liouville Volterra-Stieltjes Quadratic Delay Integral Equations (pp. 115-132)

Chapter 6 - Fractional Order Riemann-Liouville Integro-Differential Equations (pp. 133-152)

Chapter 7 - Fractional Order Riemann-Liouville Delay Integro-Differential Equations (pp. 153-182)

Chapter 8 - Abstract Integral Equations (pp. 183-190)

Chapter 9 - Abstract Integro-Differential Equations (pp. 191-214)

Chapter 10 - Abstract Integro-Differential Inclusions (pp. 215-234)

Chapter 11 - Weak Solutions for Nonlinear Fractional Differential Equations (pp. 235-280)

Chapter 12 - Weak Solutions for Nonlinear Fractional Differential Inclusions (pp. 281-292)

Chapter 13 - Ulam Stabilities for the Darboux Problem for Partial Fractional Differential Equations and Inclusions (pp. 293-322)

Appendix

References

Index

This book has been reviewed in Zentralblatt MATH -

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