Unique positive solution for a nonlinear p-Laplacian Hadamard fractional differential boundary value problem

Zichun Wang; Kemei Zhang; Zichun Wang; Kemei Zhang

doi:10.3934/era.2025209

Electronic Research Archive

2025, Volume 33, Issue 8: 4658-4678. doi: 10.3934/era.2025209

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Unique positive solution for a nonlinear p-Laplacian Hadamard fractional differential boundary value problem

Zichun Wang ,
Kemei Zhang ^,

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received: 06 June 2025 Revised: 30 July 2025 Accepted: 05 August 2025 Published: 12 August 2025

The purpose of this article is to investigate a class of nonlinear p-Laplacian Hadamard fractional differential equations. By employing two fixed–point theorems of the sum operator, we get the uniqueness of a positive solution for such p-Laplacian equations. In addition, an iterative sequence can be constructed to approximate the unique positive solution. The validity of the results is demonstrated through two illustrative numerical examples in the final of this paper.
- fixed point theorem,
- uniqueness,
- fractional differential equations,
- p-Laplacian operator
Citation: Zichun Wang, Kemei Zhang. Unique positive solution for a nonlinear p-Laplacian Hadamard fractional differential boundary value problem[J]. Electronic Research Archive, 2025, 33(8): 4658-4678. doi: 10.3934/era.2025209

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Abstract

The purpose of this article is to investigate a class of nonlinear p-Laplacian Hadamard fractional differential equations. By employing two fixed–point theorems of the sum operator, we get the uniqueness of a positive solution for such p-Laplacian equations. In addition, an iterative sequence can be constructed to approximate the unique positive solution. The validity of the results is demonstrated through two illustrative numerical examples in the final of this paper.

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