Multiple Positive Solutions for a System of Nonlinear Caputo-Type Fractional Differential Equations

Hongyu Li,Yang Chen

doi:10.1155/2020/2437530

Abstract

By using fixed-point index theory, we consider the existence of multiple positive solutions for a system of nonlinear Caputo-type fractional differential equations with the Riemann-Stieltjes boundary conditions.

Highlights

Fractional order calculus is more widely used than integer order calculus
Many researchers have been focused on the study of the existence of positive solutions for various fractional differential equations with some boundary conditions
Hao et al [32] have studied a system of fractional boundary value problems with two parameters; by using the Guo-Krasnosel’skii fixed-point theorem, they obtained the existence of positive solutions for the system in terms of different values of parameters

Summary

Introduction

Many researchers have been focused on the study of the existence of positive solutions for various fractional differential equations with some boundary conditions. By using the Guo-Krasnosel’skii fixed-point theorem, they proved that the fractional differential equation has at least a positive solution when μ satisfies some conditions. Hao et al [32] have studied a system of fractional boundary value problems with two parameters; by using the Guo-Krasnosel’skii fixed-point theorem, they obtained the existence of positive solutions for the system in terms of different values of parameters. A few researchers have been considering the systems for nonlinear integer order boundary value problems, such as in [33], where the researchers considered the existence of multiple positive solutions for a system of nonlinear third-order differential equations. The main purpose of this paper is that we prove that system (2) has one and multiple positive solutions by the fixedpoint index theory

Preliminaries

Main Results

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Applications