Existence of Solutions to a System of Riemann-Liouville Fractional Differential Equations with Coupled Riemann-Stieltjes Integrals Boundary Conditions

Abstract

A general system of fractional differential equations with coupled fractional Stieltjes integrals and a Riemann–Liouville fractional integral in boundary conditions is studied in the context of pattern formation. We need to transform the fractional differential system into the corresponding integral operator to obtain the existence and uniqueness of solutions for the system. The contraction mapping principle in Banach space and the alternative theorem of Leray–Schauder are applied. Finally, we give two applications to illustrate our theoretical results.

Keywords

• coupled system
• Riemann–Liouville fractional derivative
• contraction mapping principle in Banach space
• alternative theorem of Leray–Schauder