Existence and uniqueness results for a mixed p-Laplacian boundary value problem involving ψ-fractional derivatives and integrals

Abstract

This paper is concerned with a mixed p-Laplacian boundary value problem involving right-sided and left-sided fractional derivatives and left-sided integral operators with respect to a power function. We prove the uniqueness of solutions for the given problem with the cases 1 < p ≤ 2 by applying an efficient novel approach together with the Banach contraction mapping principle. Estimates for Green’s functions appearing in the solution of the problem at hand are also presented. Also using Brouwer fixed point theorem, existence result has been achieved for given problem.