Unique iterative positive solutions for a singular p-Laplacian fractional differential equation system with infinite-point boundary conditions

Limin Guo,Lishan Liu

doi:10.1186/s13661-019-1227-8

Abstract

By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is derived and some useful properties of the Green’s function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the positive solutions for the boundary value problem are established. Moreover, the unique positive solution that we obtained in this paper is dependent on lambda ,mu , and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.

Highlights

Fractional calculus has been shown to be more accurate and realistic than integer order models, and it provides an excellent tool to describe the hereditary properties of materials and processes, in viscoelasticity, electrochemistry, porous media, and so on
In order to meet the needs, the p-Laplacian equation is introduced in some boundary value problems, fractional differential equation system of p-Laplacian, and we refer the reader to [3, 9,10,11,12, 15, 17, 22, 24, 28, 30, 31, 35,36,37, 41] for some relevant work
There are a lot of methods to study fractional differential equations such as mixed monotone operator

Summary

Introduction

Fractional calculus has been shown to be more accurate and realistic than integer order models, and it provides an excellent tool to describe the hereditary properties of materials and processes, in viscoelasticity, electrochemistry, porous media, and so on. There are a lot of methods to study fractional differential equations such as mixed monotone operator Motivated by the excellent results above, in this paper, we consider the following infinite-point singular p-Laplacian fractional differential equation boundary value system:

Results

Conclusion