On the Existence of Solutions to a Fractional Hybrid Thermostat Model

Abstract

This work is concerned with the existence of solutions to a nonlinear fractional hybrid thermostat model in the settings of Atangana-Baleanu derivatives. We also consider the boundary conditions of this model in the form of hybrid conditions. Imposing some suitable conditions on the given data, we establish the existence result of continuous solutions based on the Dhage fixed-point theorem in Banach algebra. Moreover, an example is constructed to illustrate our theoretical result.