Notes on Krasnoselskii-type fixed-point theorems and their application to fractional hybrid differential problems

Abstract

In this paper we prove a new version of Kransoselskii's fixed-point theorem under a ($ψ, θ, \varphi$)-weak contraction condition. The theoretical result is applied to prove the existence of a solution of the following fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators orders of $0<α<1$ and $β>0:$