Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions

Abstract

Abstract We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t = 0 $t=0$ , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.

Keywords

• Singular boundary value problem
• Fractional differential equation
• Integral boundary condition
• Fixed point theorem