On a nonlinear coupled system of differential equations involving Hilfer fractional derivative and Riemann-Liouville mixed operators with nonlocal integro-multi-point boundary conditions

Abstract

We study a coupled system of multi-term Hilfer fractional differential equations of different orders involving non-integral and autonomous type Riemann-Liouville mixed integral nonlinearities supplemented with nonlocal coupled multi-point and Riemann-Liouville integral boundary conditions. The uniqueness result for the given problem is based on the contraction mapping principle, while the existence results are derived with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}$'s fixed point theorem and Leray-Schauder nonlinear alternative. Examples illustrating the main results are presented.

Keywords

• hilfer fractional differential equations
• riemann-liouville mixed integral operators
• nonlocal boundary conditions
• fixed point theorems