On a (k;chi)-Hilfer fractional system with coupled nonlocal boundary conditions including various fractional derivatives and Riemann–Stieltjes integrals

Abstract

In the present research, we investigate the existence and uniqueness of solutions for a system of (k; χ)-Hilfer fractional differential equations, subject to coupled nonlocal boundary conditions, which contain various fractional derivatives and Riemann–Stieltjes integrals. The uniqueness result relies on the Banach contraction mapping principle, while the existence results depend on the Leray–Schauder alternative and Krasnosel’skiĭ fixed point theorem. Examples are also constructed to illustrate the obtained results.

Keywords

• systems of Hilfer fractional differential equations
• fractional integrals
• coupled nonlocal boundary conditions
• existence of solutions
• Riemann–Stieltjes integrals