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

Abbas, Said/ Benchohra, Mouffak/ Graef, John R.

De Gruyter（2018発売）

• 製本 Hardcover:ハードカバー版
• 商品コード 9783110553130

Description

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

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

S. Abbas, U. Saïda, Algeria; M. Benchohra, U. Sidi Bel-Abbès, Algeria; J. R. Graef, U. Tennessee, USA; J. Henderson, Baylor U., USA.

"The book is interestingly and carefully written and would be a valuable addition to the library of all those interested in the analysis of fractional differential and integral equations and dynamical systems."
Bo Zhang in: Mathematical Reviews Clippings May 2019 MR3791511

"The book is concise and includes many examples to illustrate different approaches of existence and stability of solutions of NIFDE [nonlinear implicit fractional differential equations]. It may be recommended for graduate students or for researchers who work on analysis of solutions of fractional dynamical systems." Zentralblatt für Mathematik