Solvability of differential equations of order 2 < alpha <= 3 involving the p-Laplacian operator with boundary conditions

Abstract

In this paper, we study the existence of solutions for non-linear fractional differential equations of order 2 < α ≤ 3 involving the p-Laplacian operator with various boundary value conditions including an anti-periodic case. By using the Banach contraction mapping principle, we prove that, under certain conditions, the suggested non-linear fractional boundary value problem involving the p-Laplacian operator has a unique solution for both cases of 0 < p < 1 and p ≥ 2. Finally, we illustrate our results with some examples.