Existence results for hybrid differential equation with generalized fractional derivative

Abstract

This article deals with some existence results for fractional order hybrid differential equations involving Katugampola fractional derivative in Caputo sense. Here the Katugampola fractional derivative is generalization of two familiar fractional derivatives, namely, the Riemann-Liouville and the Hadamard fractional derivatives into a single form. Our investigations are based upon Dhage fixed point theorem, which is used to obtain the sufficient conditions for existence of at least one solution for the proposed problem.