Existence and stability of solutions of totally nonlinear neutral Caputo q-fractional difference equations

This paper investigates the existence and stability of solutions for a class of totally nonlinear neutral Caputo q-fractional difference equations of order \(0<α<1\). By transforming the equation into an equivalent integral equation and leveraging the Krasnoselskii-Burton fixed point theorem, we establish sufficient conditions for the existence of solutions. The methodology involves decomposing the integral operator into a sum of a compact operator and a large contraction. Furthermore, suitable conditions for the stability of these solutions are derived. Our theoretical results extend and generalize previous findings in the literature. An illustrative example is provided to demonstrate the applicability of the main theorems.