Positive solutions in the space of Holder functions to a fractional thermostat model

Abstract

In this paper, we study the existence of positive solutions for a nonlocal fractional boundary value problem which can be considered as the fractional analog of the thermostat model. Our solutions are placed in the space of Holder functions and the main tools used in the proof of the results are a sufficient condition about the relative compactness in Holder spaces and the classical Schauder fixed point theorem.