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 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.