Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability

Computers & Technology

Aḥmad, Bashīr

Abbas, Saïd

Benchohra, Mouffak

Salim, Abdelkrim

Software

Morgan Kaufmann

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.

Topics in Fractional Differential Equations (Developments in Mathematics, Vol. 27) (Developments in Mathematics, 27)

Science & Math

N'Guérékata, Gaston M.

Mathematics

Springer

This is devoted to exploration of the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative.

Topics in Fractional Differential Equations (Developments in Mathematics, 27)

This book deals with existence and stability issues for solutions to initial and boundary value problems for functional differential and integral equations and inclusions with Caputo's fractional derivative and Hadamard's fractional integral. 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.

Implicit Fractional Differential and Integral Equations: Existence and Stability (De Gruyter Series in Nonlinear Analysis and Applications, 26)

Graef, John R.

Henderson, Johnny

de Gruyter

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.

Advanced Functional Evolution Equations and Inclusions (Developments in Mathematics, 39)

Reference

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 Differential Equations And Inclusions: Classical And Advanced Topics (Series On Analysis, Applications And Computation)

ZHOU, YONG

Lazreg, Jamal Eddine

Nieto, Juan J

WSPC

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