Existence Results for a Class of p-Laplacian Fractional Differential Equations with Integral Boundary Conditions

Sunae Pak,Kumsong Jong,Huichol Choi,Kyunam O

doi:10.1155/2020/7129796

Abstract

In this paper, we investigate the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear fractional differential equations with p-Laplacian operator. We obtain some existence and uniqueness results concerned with our problem by using Schaefer’s fixed-point theorem and Banach contraction mapping principle. Finally, we present some examples to illustrate our main results.

Highlights

This paper deals with the existence and uniqueness of solutions for the following fractional integral boundary value problem with p-Laplacian operator: 8 >>>>>>>>>>>>>: φp ðc Dα0+xð0ÞÞ =φpðcDα0+xð1ÞÞ ð1 hðsÞφp ðcDα0+xðsÞÞds, ð1Þ where 1 < α, β ≤ 2, 3 < α + β < 4, cDα0+ and cDβ0+ are the Caputo fractional derivatives, f ∈ Cð1⁄20, 1 × R, RÞ, g, h ∈ Cð1⁄20, 1, RÞ, and the p-Laplacian operator is defined as φpðsÞ = jsjp−2s, p > 1
We investigate the existence and uniqueness of solutions for a class of integral boundary value problems of nonlinear fractional differential equations with p-Laplacian operator
>>>>>>>: φp ðc ð1 hðsÞφp ðc where 1 < α, β ≤ 2, 3 < α + β < 4, cDα0+ and cDβ0+ are the Caputo fractional derivatives, f ∈ Cð1⁄20, 1 × R, RÞ, g, h ∈ Cð1⁄20, 1, RÞ, and the p-Laplacian operator is defined as φpðsÞ = jsjp−2s, p > 1

Summary

Introduction

This paper deals with the existence and uniqueness of solutions for the following fractional integral boundary value problem with p-Laplacian operator:. Jong [15] established the existence and uniqueness of positive solutions for multipoint boundary value problems of nonlinear fractional differential equations with p-Laplacian operator by using the Banach contraction mapping principle. Summarizing previous results, very few papers dealt with the existence of solutions for integral boundary value problems of p-Laplacian fractional differential equations, especially, Zhang and Cui [22] who established the existence of positive solutions for fourth-order singular p-Laplacian differential equations under p ≥ 2 and Jiang [20] who considered the existence of solutions for nonlinear multiterm fractional differential equations with 0 < β ≤ 1. Zhang and Cui [22] investigated the existence of positive solutions for nonlinear fourth-order singular p-Laplacian differential equations with the integral boundary conditions

Preliminaries

Main Results

Examples