Unique positive solution for a <em>p</em>-Laplacian fractional differential boundary value problem involving Riemann-Stieltjes integral

Chengbo Zhai; Yuanyuan Ma; Hongyu Li; Chengbo Zhai; Yuanyuan Ma; Hongyu Li

doi:10.3934/math.2020304

AIMS Mathematics

2020, Volume 5, Issue 5: 4754-4769. doi: 10.3934/math.2020304

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Research article

Unique positive solution for a p-Laplacian fractional differential boundary value problem involving Riemann-Stieltjes integral

1.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P.R. China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

Received: 01 April 2020 Accepted: 12 May 2020 Published: 01 June 2020
MSC : 34B18, 34B15, 26A33

In this article, we study a class of p-Laplacian fractional differential boundary value problem involving Riemann-Stieltjes integral. By two fixed point theorems of a sum operator in partial ordering Banach spaces, we get the existence and uniqueness of positive solutions for addressed problem. Moreover, we can make iterative sequences to approximate the unique positive solution. In addition, two examples are given to illustrate the main results.
- positive solutions,
- fractional p-Laplacian equations,
- Riemann-Stieltjes integral boundary condition
Citation: Chengbo Zhai, Yuanyuan Ma, Hongyu Li. Unique positive solution for a p-Laplacian fractional differential boundary value problem involving Riemann-Stieltjes integral[J]. AIMS Mathematics, 2020, 5(5): 4754-4769. doi: 10.3934/math.2020304

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Abstract

In this article, we study a class of p-Laplacian fractional differential boundary value problem involving Riemann-Stieltjes integral. By two fixed point theorems of a sum operator in partial ordering Banach spaces, we get the existence and uniqueness of positive solutions for addressed problem. Moreover, we can make iterative sequences to approximate the unique positive solution. In addition, two examples are given to illustrate the main results.

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