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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.
Sommario
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
Info autore
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.
