Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions

Jingli Xie,Lijing Duan

doi:10.1155/2020/4739175

Abstract

In this paper, we investigate a class of integral boundary value problems of fractional differential equations with a p-Laplacian operator. Existence of solutions is obtained by using the fixed point theorem, and an example is given to show the applicability of our main result.

Highlights

IntroductionWe consider the nonlinear fractional differential equations with a p-Laplacian operator and integral boundary conditions
In this paper, we consider the nonlinear fractional differential equations with a p-Laplacian operator and integral boundary conditions 8 >>>>>< cDβ0+ φpðcDα0+uðtÞÞ ð1 + f ðt, uðtÞÞ = 0, t ∈ 1⁄20, 1,>>>>>: uð1Þ = λ cDα0+uð1Þ uðsÞds, u′
In [15], by using the fixed point theorem, Yan et al studied the existence of solutions for boundary value problems of fractional differential equations with a p-Laplacian operator: 8 >>>

Summary

Introduction

We consider the nonlinear fractional differential equations with a p-Laplacian operator and integral boundary conditions. Some nonlinear analysis tools such as coincidence degree theory [4, 5], upper and lower solution method [6,7,8], fixed point theorems [9,10,11], and variational methods [12,13,14] have been widely used to discuss existence of solutions for boundary value problems of fractional differential equations. In [15], by using the fixed point theorem, Yan et al studied the existence of solutions for boundary value problems of fractional differential equations with a p-Laplacian operator:. We obtain the existence result of the fractional differential equations with integral boundary equations by using the Schauder fixed point theorem and other mathematical analysis techniques.

Preliminaries

Main Results

Applications