Existence and Uniqueness of Solutions for a Fractional Order Antiperiodic Boundary Value Problem with a p -Laplacian Operator

Abstract

We study the existence and uniqueness of solutions for a class of antiperiodic boundary value problems of the fractional differential equation with a $p$-Laplacian operator. Based on the Leray-Schauder nonlinear alternative, several sufficient conditions of the existence and uniqueness of solution of the above problem are established. Our results improve and complement the recent work of Chen and Liu, 2012.