Coupled systems of nonlinear sequential proportional Hilfer-type fractional differential equations with multi-point boundary conditions

Abstract

In this paper, we studied the existence of solutions for a coupled system of nonlinear sequential proportional $ \psi $-Hilfer fractional differential equations with multi-point boundary conditions. By using a Burton's version of the Krasnosel'ski$\breve{{\rm{i}}}$'s fixed-point theorem we established sufficient conditions for the existence result. An example illustrating our main result was also provided.

Keywords

• coupled system
• hilfer fractional proportional derivative
• multi-point boundary conditions
• fixed-point theorem