Degree theory and existence of positive solutions to coupled system involving proportional delay with fractional integral boundary conditions

Abstract

The purpose of this paper is to obtain the existence of at least one solution to the following coupled system of nonlinear fractional order differential equations under the integral type boundary conditions by using topological degree theory where , , denotes the standard Caputo fractional derivative, , and are continuous functions. For this intention, some results for the existence of at least one solution are constructed. For the validity of our results, an appropriate example is presented.