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Fractional Difference, Differential Equations, and Inclusions
Analysis and Stability
- 1st Edition - January 11, 2024
- Authors: Saïd Abbas, Bashir Ahmad, Mouffak Benchohra, Abdelkrim Salim
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 3 6 0 1 - 3
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 3 6 0 2 - 0
Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stabil… Read more
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Request a sales quoteFractional 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.
- 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
Researchers in computational modelling, applied mathematicians, and computer scientists working with researchers and developers in engineering, biomedical, and other applied sciences. Researchers, developers, and graduate students in mathematics interested in fractional differential equations and inclusions
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Biography
- Saïd Abbas
- Bashir Ahmad
- Mouffak Benchohra
- Abdelkrim Salim
- Preface
- 1: Introduction
- Abstract
- References
- 2: Preliminary background
- Abstract
- 2.1. Notations and definitions
- 2.2. Elements from fractional calculus theory
- 2.3. Fractional q-calculus
- 2.4. Multi-valued analysis
- 2.5. Measure of noncompactness
- 2.6. Measure of weak noncompactness
- 2.7. Degree of nondensifiability
- 2.8. Some attractivity concepts
- 2.9. Some Ulam stability concepts
- 2.10. Some fixed-point theorems
- 2.11. Auxiliary lemmas
- References
- 3: Caputo fractional difference equations in Banach spaces
- Abstract
- 3.1. Implicit fractional q-difference equations in Banach spaces
- 3.2. Fractional q-difference equations on the half line
- 3.3. On the solution of Caputo fractional q-difference equations in Banach spaces
- 3.4. Notes and remarks
- References
- 4: Caputo fractional difference inclusions
- Abstract
- 4.1. Fractional q-difference inclusions in Banach spaces
- 4.2. Weak solutions for Pettis fractional q-difference inclusions
- 4.3. Upper and lower solutions for fractional q-difference inclusions
- 4.4. Notes and remarks
- References
- 5: Ulam stability for fractional difference equations
- Abstract
- 5.1. Existence and Ulam stability for implicit fractional q-difference equations
- 5.2. Ulam stability results
- 5.3. Implicit fractional q-difference equations: analysis and stability
- 5.4. Uniqueness and Ulam stability for implicit fractional q-difference equations via Picard operators theory
- 5.5. Notes and remarks
- References
- 6: Impulsive fractional difference equations
- Abstract
- 6.1. Impulsive implicit Caputo fractional q-difference equations
- 6.2. Implicit Caputo fractional q-difference equations with noninstantaneous impulses
- 6.3. Instantaneous and noninstantaneous impulsive integro-differential equations in Banach spaces
- 6.4. Notes and remarks
- References
- 7: Coupled fractional difference systems
- Abstract
- 7.1. Implicit coupled Caputo fractional q-difference systems
- 7.2. Existence and oscillation for coupled fractional q-difference systems
- 7.3. Notes and remarks
- References
- 8: Coupled Caputo–Hadamard fractional differential systems in generalized Banach spaces
- Abstract
- 8.1. Coupled Caputo–Hadamard fractional differential systems with multipoint boundary conditions
- 8.2. Random coupled Caputo–Hadamard fractional differential systems with four-point boundary conditions
- 8.3. Random coupled systems of implicit Caputo–Hadamard fractional differential equations with multi-point boundary conditions
- 8.4. Notes and remarks
- References
- 9: Coupled Hilfer–Hadamard fractional differential systems in generalized Banach spaces
- Abstract
- 9.1. Coupled Hilfer and Hadamard fractional differential systems
- 9.2. Coupled Hilfer and Hadamard random fractional differential systems with finite delay
- 9.3. Random coupled Hilfer and Hadamard fractional differential systems
- 9.4. Notes and remarks
- References
- 10: Oscillation and nonoscillation results for fractional q-difference equations and inclusions
- Abstract
- 10.1. Oscillation and nonoscillation results for Caputo fractional q-difference equations and inclusions
- 10.2. Existence and oscillation for coupled fractional q-difference systems
- 10.3. Notes and remarks
- References
- 11: A Filippov's theorem and topological structure of solution sets for fractional q-difference inclusions
- Abstract
- 11.1. Existence and topological structure of solution sets
- 11.2. Filippov theorem
- 11.3. Notes and remarks
- References
- 12: On ψ-Caputo fractional differential equations in Banach spaces
- Abstract
- 12.1. Boundary value problem for fractional differential equations via densifiability techniques
- 12.2. Application of Meir–Keeler condensing operators
- 12.3. Notes and remarks
- References
- 13: Ulam stability for ψ-Caputo fractional differential equations and systems
- Abstract
- 13.1. Existence and Mittag–Leffler–Ulam stability of fractional partial differential equations
- 13.2. Coupled system of fractional differential equations without and with delay in generalized Banach spaces
- 13.3. Coupled system of nonlinear hyperbolic partial fractional differential equations in generalized Banach spaces
- 13.4. Notes and remarks
- References
- 14: Monotone iterative technique for ψ-Caputo fractional differential equations
- Abstract
- 14.1. Initial value problem for nonlinear ψ-Caputo fractional differential equations
- 14.2. Sequential ψ-Caputo fractional differential equations with nonlinear boundary conditions
- 14.3. Hyperbolic fractional partial differential equation
- 14.4. Notes and remarks
- References
- References
- References
- Index
- No. of pages: 398
- Language: English
- Edition: 1
- Published: January 11, 2024
- Imprint: Morgan Kaufmann
- Paperback ISBN: 9780443236013
- eBook ISBN: 9780443236020
SA
Saïd Abbas
Dr. Saïd 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.
Affiliations and expertise
Professor, Department of Mathematics, Tahar Moulay University of Saida, AlgeriaBA
Bashir Ahmad
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.
Affiliations and expertise
Professor, King Abdulaziz University, Jeddah, Saudi ArabiaMB
Mouffak Benchohra
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.
Affiliations and expertise
Professor, Department of Mathematics, Djillali Liabes University of Sidi Bel Abbes, AlgeriaAS
Abdelkrim Salim
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.
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