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

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 Krasnoserskii's fixed point theorem and Leray-Schauder nonlinear alternative. Examples illustrating the main results are presented.

Automated summary

This study investigates a coupled system of multi-term Hilfer fractional differential equations with different orders. The system involves non-integral and autonomous type Riemann-Liouville mixed integral nonlinearities, as well as nonlocal coupled multi-point and Riemann-Liouville integral boundary conditions. The uniqueness result is established using the contraction mapping principle, while the existence results are derived with the help of Krasnoserskii's fixed point theorem and Leray-Schauder nonlinear alternative. Examples are presented to illustrate the main findings.