Existence and uniqueness of solutions for mixed fractional q-difference boundary value problems

Abstract

Abstract In this paper, we investigate the existence and uniqueness of solutions for mixed fractional q-difference boundary value problems involving the Riemann–Liouville and the Caputo fractional derivative. By using the Guo–Krasnoselskii fixed point theorem and Banach contraction mapping principle as well as Schaefer’s fixed point theorem, we obtain the main results. In addition, several examples are given to illustrate the main results.

Keywords

• Boundary value problem
• Fractional q-difference equations
• Existence and uniqueness