On the Solvability of Caputo q-Fractional Boundary Value Problem Involving p-Laplacian Operator

Abstract

We consider the model of a Caputo q-fractional boundary value problem involving p-Laplacian operator. By using the Banach contraction mapping principle, we prove that, under some conditions, the suggested model of the Caputo q-fractional boundary value problem involving p-Laplacian operator has a unique solution for both cases of 0 < p < 1 and p > 2. It is interesting that in both cases solvability conditions obtained here depend on q, p, and the order of the Caputo q-fractional differential equation. Finally, we illustrate our results with some examples.