Existence and Uniqueness of Some Cauchy Type Problems in Fractional q-Difference Calculus

Abstract

This thesis aims to study and analysis of several results concerning the existence, uniqueness, and stability of solutions for nonlinear fractional qdifferential equations with initial and boundary conditions, using fractional qderivatives of Caputo, Katugampola and Hilfer-Katugampola. In addition, the stability of fractional-order systems is studied using the direct Lyapunov method. The results have been proved using some fixed-point theorems of Schauder, Banach’s contraction principle, and the nonlinear alternative technique of Leray-Schauder.