Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator

Abstract

This paper is concerned with an integral boundary value problem of fractional differential equations with p-Laplacian operator. Sufficient conditions ensuring the existence of extremal solutions for the given problem are obtained. Our results are based on the method of upper and lower solutions and monotone iterative technique.

Monotone iterative solutions for a coupled system of p-Laplacian differential equations involving the Riemann–Liouville fractional derivative

“…In particular, much effort has been made toward the study of the existence of solutions for fractional differential equations with p-Laplacian operator [1][2][3][4][5][6][7][8]. The monotone iterative technique, combined with the method of upper and lower solutions, is a powerful tool for proving the existence of solutions of nonlinear differential equations; see [9,10] and the references therein. However, only a few papers considered the upper an lower solutions method and the monotone iteration technique for p-Laplacian boundary value problems with fractional coupled systems.…”