Positive Solutions for a System of Fractional Differential Equations with Two Parameters

Hongyu Li,Junting Zhang

doi:10.1155/2018/1462505

Abstract

In this paper, the existence of positive solutions in terms of different values of two parameters for a system of conformable-type fractional differential equations with the p-Laplacian operator is obtained via Guo-Krasnosel’skii fixed point theorem.

Highlights

We study the existence of positive solutions for the following system of fractional differential equations: Dα1 (φp1 (Dα1x (t))) = λg (t, x (t), y (t)), 0 < t < 1, (1)
Most results have adopted the Riemann-Liouville and Caputo-type fractional derivatives; we can see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] and the references therein; for example, in [28], by using Guo-Krasnosel’skii fixed point theorem, the authors obtained the various existence results for positive solutions about a system of Riemann-Liouville type fractional boundary value problems with two parameters and the p-Laplacian operator. There is another kind of fractional derivative which is conformable fractional derivative
In [29], the authors Khalil R. et al first introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. They first presented the definition of conformable fractional derivative of order α ∈

Summary

Introduction

Most results have adopted the Riemann-Liouville and Caputo-type fractional derivatives; we can see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] and the references therein; for example, in [28], by using Guo-Krasnosel’skii fixed point theorem, the authors obtained the various existence results for positive solutions about a system of Riemann-Liouville type fractional boundary value problems with two parameters and the p-Laplacian operator.

Preliminaries

Main Results

Conclusion