Positive Solutions for Higher-Order Nonlinear Fractional Differential Equations

Abstract

This paper investigates the existence of positive solutions for a class of higher-order nonlinear fractional differential equations with initial conditions given for ordinary as well as fractional derivatives of the unknown function. We assume that the nonlinear term f involves also derivatives of fractional order. The results are established by converting the problem into an equivalent integral equation and applying Guo–Krasnoselskii’s fixed-point theorem in cones.