Existence of positive solutions for integral boundary value problems of fractional differential equations with p-Laplacian

Luchao Zhang,Xiping Liu,Weiguo Zhang,Mei Jia

doi:10.1186/s13662-017-1086-5

Abstract

This paper is concerned with the existence of positive solutions for integral boundary value problems of Caputo fractional differential equations with p-Laplacian operator. By means of the properties of the Green’s function, Avery-Peterson fixed point theorems, we establish conditions ensuring the existence of positive solutions for the problem. As an application, an example is given to demonstrate the main result.

Highlights

Fractional differential equations have been proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering, such as rheology, dynamical processes in self-similar and porous structures, heat conduction, control theory, electroanalytical chemistry, chemical physics, economics, etc
Many papers and books have appeared on fractional calculus and fractional differential equations
In [ ], Liu et al studied the solvability of the Caputo fractional differential equation with boundary value conditions involving the p-Laplacian operator

Summary

Introduction

Fractional differential equations have been proved to be valuable tools in the modeling of many phenomena in various fields of science and engineering, such as rheology, dynamical processes in self-similar and porous structures, heat conduction, control theory, electroanalytical chemistry, chemical physics, economics, etc. There are few studies of the existence of positive solution of fractional differential equations with the p-Laplacian operator; see [ – ] and the references therein. In [ ], Liu et al studied the solvability of the Caputo fractional differential equation with boundary value conditions involving the p-Laplacian operator.

Results

Conclusion