Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem

Xinguang Zhang,Hua Su,Cuiling Mao,Yonghong Wu

doi:10.1155/2014/457965

Abstract

We establish the existence of positive solutions to a class of singular nonlocal fractional order differential system depending on two parameters. Our methods are based on Schauder’s fixed point theorem.

Highlights

Differential equations of fractional order have recently proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering
Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of many materials and processes
Motivated by the results mentioned above, in this paper, we study the existence of positive solutions for the following singular

Summary

Introduction

Differential equations of fractional order have recently proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of many materials and processes. In [18], Zhang et al discussed the existence and uniqueness of positive solutions for the following fractional differential equation with derivatives:. By means of monotone iterative technique, the existence and uniqueness of the positive solution for a fractional differential equation with derivatives are established, and the iterative sequence of the solution, an error estimation, and the convergence rate of the positive solution are given. Motivated by the results mentioned above, in this paper, we study the existence of positive solutions for the following singular. Abstract and Applied Analysis nonlocal fractional order differential system depending on two parameters:.

Preliminaries and Lemmas

Main Result