The existence and uniqueness of positive solution for nonlinear singular fractional differential equations with integro-differential boundary value conditions

Abstract

In this paper, we consider a class of singular nonlinear higher-order fractional equation supplemented with integro-differential boundary conditions. The fractional derivative of different orders are involved in the nonlinear terms and boundary conditions. Transform the higher-order fractional differential equation into the lower-order fractional differential equation is the main difficulty. Existence and uniqueness are obtained by the sum-type fixed point theorems on cone.