Existence and Stability Results for Fractional Hybrid q-Difference Equations with q-Integro-Initial Condition

This article is concerned with the study of a new class of hybrid fractional q-integro-difference equations involving Caputo type q-derivatives and Riemann-Liouville q-integrals of different orders with a nonlocal q-integro-initial condition. An existence result for the given problem is obtained by means of Krasnoselskii’s fixed point theorem, whereas the uniqueness of its solutions is shown by applying the Banach contraction mapping principle. We also discuss the stability of solutions of the problem at hand and find that it depends on the nonlocal parameter in contrast to the initial position of the domain. To demonstrate the application of the obtained results, examples are constructed.