
Fractional Difference, Differential Equations, and Inclusions
Analysis and Stability
Morgan Kaufmann (Publisher)
Published on 16. January 2024
Book
Paperback/Softback
300 pages
978-0-443-23601-3 (ISBN)
Description
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. Covered equations include delay effects of finite, infinite, or state-dependent nature, and 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. 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. All abstract results in the book are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences.
More details
Language
English
Place of publication
San Francisco
United States
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 235 mm
Width: 191 mm
Weight
820 gr
ISBN-13
978-0-443-23601-3 (9780443236013)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Saïd Abbas | Bashir Ahmad | Mouffak Benchohra
Fractional Difference, Differential Equations, and Inclusions
Analysis and Stability
E-Book
01/2024
Morgan Kaufmann
€160.00
Available for download
Persons
Dr. Said Abbas is a Full Professor at the Department of Mathematics at Tahar Moulay University of Saida, Algeria. Dr. Abbas received his MSc in Functional Analysis from Mostaganem University, Algeria, and his PhD in Differential Equations from Djillali Liabes University of Sidi Bel Abbes, Algeria. His research fields include fractional differential equations and inclusions, evolution equations and inclusions, control theory and applications, and other topics in applied mathematics. Dr. Abbas is the author of Topics in Fractional Differential Equations, Springer; Advanced Functional Evolution Equations and Inclusions, Springer; Fractional Differential Equations and Inclusions: Classical and Advanced Topics, World Scientific; and Implicit Fractional Differential and Integral Equations, DeGruyter. Dr. Bashir Ahmad is a Full Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He received his Ph.D. from Quaid-i-Azam University, Islamabad, Pakistan. His research interest includes approximate/numerical methods for nonlinear problems involving a variety of differential equations, existence theory of fractional differential equations, stability and instability properties of dynamical systems, impulsive systems, control theory, mathematical biology, and fluid mechanics. He was honored with "Best Researcher of King Abdulaziz University? award in 2009. He is the Managing Editor of Bulletin of Mathematical Sciences, Editor-in-Chief of the journal Fractional Differential Calculus, and member of editorial boards of several journals. He has been "Highly-Cited Researcher? in the category of Mathematics (Web of Science/Clarivate Analytics) from 2014 to 2019. Dr. Mouffak Benchohra is a Full Professor in the Department of Mathematics, Djillali Liabes University of Sidi Bel Abbes. Dr. Benchohra received his MSc in Nonlinear Analysis from Tlemcen University, Algeria, and his PhD in Mathematics from Djillali Liabes University, Sidi Bel Abbes, Algeria. His research fields include fractional differential equations, evolution equations and inclusions, control theory and applications, and other topics in applied mathematics. Dr. Benchohra is the author of Topics in Fractional Differential Equations, Springer; Advanced Functional Evolution Equations and Inclusions, Springer; Fractional Differential Equations and Inclusions: Classical and Advanced Topics, World Scientific; and Implicit Fractional Differential and Integral Equations, DeGruyter.
He is a Highly Cited Researcher in Mathematics from Thompson Reuters (2014) and Clarivate Analytics (2017 and 2018). He is also among the top 2% researchers in the world (2020, 2021, 2022) released by Stanford University. Dr. Benchohra has also been the chair of the Department of Mathematics at Djillali Liabes University, Sidi Bel Abbes, and he serves on the Editorial Board of 10 international journals. Dr. Abdelrkim Salim is an Associate Professor at the Faculty of Technology, Hassiba Benbouali University of Chlef, Algeria. Salim received his MSc in functional analysis and differential equations, and his PhD in mathematical analysis and applications from Djillali Liabes University of Sidi Bel Abbes, Algeria. His research fields include fractional differential equations and inclusions, control theory and applications, and other topics in applied mathematics.
He is a Highly Cited Researcher in Mathematics from Thompson Reuters (2014) and Clarivate Analytics (2017 and 2018). He is also among the top 2% researchers in the world (2020, 2021, 2022) released by Stanford University. Dr. Benchohra has also been the chair of the Department of Mathematics at Djillali Liabes University, Sidi Bel Abbes, and he serves on the Editorial Board of 10 international journals. Dr. Abdelrkim Salim is an Associate Professor at the Faculty of Technology, Hassiba Benbouali University of Chlef, Algeria. Salim received his MSc in functional analysis and differential equations, and his PhD in mathematical analysis and applications from Djillali Liabes University of Sidi Bel Abbes, Algeria. His research fields include fractional differential equations and inclusions, control theory and applications, and other topics in applied mathematics.
Author
Professor, Department of Mathematics, Tahar Moulay University of Saida, Algeria
Professor, King Abdulaziz University, Jeddah, Saudi Arabia
Professor, Department of Mathematics, Djillali Liabes University of Sidi Bel Abbes, Algeria
Content
1. Preliminary Background
2. Caputo Fractional Difference Equations in Banach Spaces
3. Caputo Fractional Difference Inclusions
4. Ulam Stability for Fractional Difference Equations
5. Impulsive Fractional Difference Equations
6. Coupled Fractional Difference Systems
7. Coupled Caputo-Hadamard Fractional Differential Systems in Generalized Banach Spaces
8. Coupled Hilfer-Hadamard Fractional Differential Systems in Generalized Banach Spaces
9. Oscillation and Nonoscillation Results for Fractional q-Difference Equations and Inclusions
10. A Filippov's Theorem and Topological Structure of Solution Sets for Fractional q-Difference Inclusions
11. On ? -Caputo Fractional Differential Equations in Banach Spaces
12. Ulam Stability for ? -Caputo Fractional Differential Equations and Systems
13. Monotone Iterative Technique for psi-Caputo Fractional Differential Equations
2. Caputo Fractional Difference Equations in Banach Spaces
3. Caputo Fractional Difference Inclusions
4. Ulam Stability for Fractional Difference Equations
5. Impulsive Fractional Difference Equations
6. Coupled Fractional Difference Systems
7. Coupled Caputo-Hadamard Fractional Differential Systems in Generalized Banach Spaces
8. Coupled Hilfer-Hadamard Fractional Differential Systems in Generalized Banach Spaces
9. Oscillation and Nonoscillation Results for Fractional q-Difference Equations and Inclusions
10. A Filippov's Theorem and Topological Structure of Solution Sets for Fractional q-Difference Inclusions
11. On ? -Caputo Fractional Differential Equations in Banach Spaces
12. Ulam Stability for ? -Caputo Fractional Differential Equations and Systems
13. Monotone Iterative Technique for psi-Caputo Fractional Differential Equations