Existence of positive solutions in the space of Lipschitz functions to a class of fractional differential equations of arbitrary order

In this paper, we study sufficient conditions for the existence of positive solutions to a class of fractional differential equations of arbitrary order. Our solutions are placed in the space of Lipschitz functions and, perhaps, this is a part of the originality of the paper. For our study, we use a recent result about the relative compactness in Hölder spaces and the classical Schauder fixed point theorem.