Multiple Positive Solutions for Fractional Three-Point Boundary Value Problem with p-Laplacian Operator

Dong Li,Yang Liu,Chunli Wang

doi:10.1155/2020/2327580

Abstract

In this paper, we investigate the existence of multiple positive solutions or at least one positive solution for fractional three-point boundary value problem with p-Laplacian operator. Our approach relies on the fixed point theorem on cones. The results obtained in this paper essentially improve and generalize some well-known results.

Highlights

Fractional calculus has been adapted to numerous fields, such as engineering, mechanics, physics, chemistry, and biology
Fractional differential equations have been found to be a powerful tool in modeling various phenomena in many areas of science and engineering such as physics, fluid mechanics, and heat conduction
Fractional-order boundary value problems involving classical, multipoint, high-order, and integral boundary conditions have extensively been studied by many researchers and a variety of results can be found in recent literature on the topic [21,22,23,24,25]

Summary

Introduction

Fractional calculus has been adapted to numerous fields, such as engineering, mechanics, physics, chemistry, and biology. In [15], Chai studied the boundary value problems of fractional differential equations with p-Laplacian operator as follows: In [16], by using Krasnosel’skii’s fixed point theorem, Tian et al obtained the existence of positive solutions for a boundary value problem of fractional differential equations with p-Laplacian operator as follows:

Results

Conclusion