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

Minghui Liu; Jiqiang Jiang; Guoqiang Chen; Na Li; Lishan Liu; Yonghong Wu; Minghui Liu; Jiqiang Jiang; Guoqiang Chen; Na Li; Lishan Liu; Yonghong Wu

doi:10.3934/era.2026080

Electronic Research Archive

2026, Volume 34, Issue 3: 1785-1808. doi: 10.3934/era.2026080

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Research article

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

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
2.
Dongying Vocational College, Dongying 257091, Shandong, China
3.
School of Mathematical Sciences, Xinjiang Normal University, Wulumuqi 830017, Xinjiang, China
4.
Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia

Received: 18 December 2025 Revised: 15 January 2026 Accepted: 06 February 2026 Published: 27 February 2026

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.
- Hadamard fractional derivative,
- fractional differential equation,
- fixed-point theorems,
- reducing order technique,
- parameter
Citation: Minghui Liu, Jiqiang Jiang, Guoqiang Chen, Na Li, Lishan Liu, Yonghong Wu. Positive solutions for Hadamard fractional differential equations with sign changing nonlinearity and paremeters[J]. Electronic Research Archive, 2026, 34(3): 1785-1808. doi: 10.3934/era.2026080

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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.

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