Well-Posedness for Fractional $(p, q)$-Difference Equations Initial Value Problem

Abstract

In this paper, we investigate a class of the fractional $(p, q)$-difference initial value problem with the fractional $(p, q)$-integral boundary conditions with the aid of the method of successive approximations(Picard method) and fractional $(p, q)$-Gronwall inequality, obtaining sufficient conditions for the existence, uniqueness and continuous dependence results of solutions.