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Research Article | Open Access

Positive solutions for Hadamard fractional differential equations with sign changing nonlinearity and paremeters

Minghui Liu1, Jiqiang Jiang1( ), Guoqiang Chen2, Na Li2, Lishan Liu1,3, Yonghong Wu4
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
Dongying Vocational College, Dongying 257091, Shandong, China
School of Mathematical Sciences, Xinjiang Normal University, Wulumuqi 830017, Xinjiang, China
Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
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Abstract

This study investigates boundary value problems for nonlinear fractional differential equations. The differential operator is interpreted in the Hadamard sense and is coupled with a nonlinear term that involves the fractional derivative of the unknown function. The existence and multiplicity of positive solutions were established by a reducing-order technique based on the Guo–Krasnoselskii fixed-point theorem. Also, some examples are presented to illustrate the validity of our main results.

Keywords

Hadamard fractional derivativefractional differential equationfixed-point theoremsreducing order techniqueparameter

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Electronic Research Archive
Volume 34 Issue 3,
March 2026
Pages 1785-1808
DOI: 10.3934/era.2026080

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Cite this article:
Liu M, Jiang J, Chen G, et al. Positive solutions for Hadamard fractional differential equations with sign changing nonlinearity and paremeters. Electronic Research Archive, 2026, 34(3): 1785-1808. https://doi.org/10.3934/era.2026080

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Received: 18 December 2025
Revised: 15 January 2026
Accepted: 06 February 2026
Published: 27 February 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)