Abstract: We studied the boundary value problem of a coupled system of a class of nonlinear Caputo type fractional differential equations with integral boundary value conditions by applying Schauder fixed point theorem, LeraySchauder choice theory and Banach fixed point theorem. We obtained sufficient conditions for the existence and uniqueness of positive solutions of the coupled system, and illustrated the applicability of the theorem by examples.

Key words: fractional differential equation, coupled system, positive solution, fixed point theorem