Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation

Abstract

We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: , where $D_{0^{+}}^{\alpha }$ denotes the standard Riemann-Liouville fractional derivative, $f:\left[\mathrm{0,1}\right]\times [0,\infty )\to [0,\infty )$ is a continuous function, $a_i\ge 0$ for $i=\mathrm{1,2},\dots ,m-2$, and . Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results.