On Positive Solutions for a Fractional Thermostat Model with a Convex–Concave Source Term via $$\psi $$-Caputo Fractional Derivative

Abstract

We consider a fractional thermostat model involving $$\psi $$-Caputo fractional derivatives. Two cases are discussed: the case when the source term is concave and the case when the source term is convex. For each case, the existence and uniqueness of positive solutions are investigated. Moreover, an iterative algorithm is provided to approximate the solutions. Our approach is based on a fixed point theorem on cones.