New results in the study of a multi-point boundary value problem with higher order Riemann-Liouville fractional derivative

Abstract

This study is concerned with a new class of fractional differential equations with arbitrary order, coupled with multi-point boundary conditions. To solve this problem, we extract the formulation of an equivalent integral equation. We establish a continuous operator within a Banach space, leveraging cone theory and fixed point theorems. These tools allow us to establish the existence of multiple solutions for our fractional boundary value problem, contingent upon certain assumptions. To conclude, we offer illustrative examples to exemplify the obtained results.