Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition

摘要

This paper deals with the following boundary value problem where is the Riemann-Liouville fractional derivative, and the nonlinearity which could be singular at both and is required to be continuous on satisfying a mild Lipschitz assumption. Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution satisfying where.