Existence and uniqueness of solutions for systems of fractional differential equations with Riemann–Stieltjes integral boundary condition

Abstract

Abstract In this article, we first establish an existence and uniqueness result for a class of systems of nonlinear operator equations under more general conditions by means of the cone theory and monotone iterative technique. Furthermore, the iterative sequence of the solution and the error estimation of the system are given. Then we use this new result to study the existence and uniqueness of the solution for boundary value problems of systems of fractional differential equations with a Riemann–Stieltjes integral boundary condition in real Banach spaces. The results obtained in this paper are more general than many previous results and complement them.

Keywords

• Systems of nonlinear binary operator equations
• Real Banach spaces
• Monotone iterative technique
• Existence and uniqueness of positive solutions
• Systems of fractional differential equations