Twin Positive Solutions of a Katugampola Fractional Boundary Value Problem

ABSTRACT This article establishes sufficient conditions for twin positive solutions to a well‐posed two‐point boundary value problem (BVP) with separated boundary conditions involving the Katugampola fractional derivative. For this purpose, we use the Avery Henderson twin fixed‐point theorem. Since the Katugampola derivative encompasses both the Riemann Liouville and the Hadamard derivatives, the results developed in this article cover the existing literature. Three examples illustrate the applicability of the obtained results. This work appears to be the first in the literature to address twin positive solutions of a Katugampola fractional BVP with separated boundary conditions.