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

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.

• 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