The Cauchy Problems for Fractional Q-Difference Equations with Integral Conditions in Banach Spaces

Abstract

In            In this paper, we investigate the existence of solutions to the fractional q-difference equation of the type   with    where  and  is a bounded linear operator on a Banach space  The operator  denotes the Caputo fractional q-derivative of order . Our existence result are obtained by using the Banach fixed point theorem  and the Schaefer fixed point theorem.