Existence and Uniqueness of Positive Solutions for Singular Nonlinear Fractional Differential Equation via Mixed Monotone Operator Method

Tian Wang,Zhaocai Hao

doi:10.1155/2020/2354927

Abstract

In this article, we discuss the existence and uniqueness of positive solution for a class of singular fractional differential equations, where the nonlinear term contains fractional derivative and an operator. By applying the fixed point theorem in cone, we get the existence and uniqueness of positive solutions for the fractional differential equation. Moreover, we give an example to demonstrate our main result.

Highlights

In this article, we consider the existence and uniqueness of solutions for the following singular fractional differential equations: 8 >>>< Dα0+ uðt Þ + pðtÞ f t, uðt Þ, Dβ0+ uðtÞ qðt
In [1,2,3,4], the authors studied the solutions of fractional differential equations, and obtained some interesting results
We focus on fractional differential equation

Summary

Introduction

We consider the existence and uniqueness of solutions for the following singular fractional differential equations:. In [1,2,3,4], the authors studied the solutions of fractional differential equations, and obtained some interesting results. Such as uniqueness of iterative positive solution, existence of multiple positive solutions or maximum and minimum solutions. In [14], by using cone expansion fixed point theorem, Li et al studied the existence of positive solutions for the following fractional differential equation with RiemannStieltjes integral:.

Preliminaries and Lemmas

Main Results

Example