Positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary conditions

Abstract

In the this paper, we establish sufficient conditions for the existence and nonexistence of positive solutions to a general class of integral boundary value problems for a coupled system of fractional differential equations. The differential operator is taken in the Riemann–Liouville sense. Our analysis rely on Banach fixed point theorem, nonlinear differentiation of Leray–Schauder type and the fixed point theorems of cone expansion and compression of norm type. As applications, some examples are also provided to illustrate our main results.