Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with  p -Laplacian Operator

Kumsong Jong,Ok Ri,Songguk Jong,Kyongjun Jang,Huichol Choi,Kyongson Jon

doi:10.1155/2021/7527306

Abstract

In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p -Laplacian operator. Using the Banach contraction mapping principle, the existence, the uniqueness, the positivity, and the continuous dependency on m -point boundary conditions of the solutions to the given problem are investigated. Also, two examples are presented to demonstrate our main results.

Highlights

This paper deals with a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p-Laplacian operator: 8 >>>>>>>>>< Dβ0+ Dγ0+ φpðDα0+xðtÞÞ =xð0Þ = 0, Dδ0+xð1Þ f À t, xðtÞ, Dγ0+ Á xðtÞ, m−2 = 〠 ξiDδ0+xðηiÞ, < t>>>>>>>>>: Dα0+xð0Þ
After analyzing the results for nonlinear multiterm fractional differential equations with p-Laplacian operator, we have found that most of these previous works only dealt with some kinds of p-Laplacian equations that had certain rules for the fractional derivatives in nonlinear source terms and were limited to the cases of two-point, three-point, and four-point boundary conditions
Motivated by the analysis mentioned above, this paper is aimed at studying some properties of positive solutions to m-point boundary value problems of nonlinear multiterm fractional differential equations with p-Laplacian operator including the existence, the uniqueness, and the continuous dependency on boundary conditions

Summary

Introduction

This paper deals with a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p-Laplacian operator:. Li and Qi [12] improved the works of Guo et al [8] to show the existence of positive solutions for the following multipoint boundary value problems of nonlinear fractional differential equations with p-Laplacian operator:. Motivated by the analysis mentioned above, this paper is aimed at studying some properties of positive solutions to m-point boundary value problems of nonlinear multiterm fractional differential equations with p-Laplacian operator including the existence, the uniqueness, and the continuous dependency on boundary conditions.

Preliminaries

Main Results

Examples

Conclusion