Investigating positive solutions in $ p $-Laplacian fractional systems with infinite-point boundaries

Doha A. Kattan; Hasanen A. Hammad; Doha A. Kattan; Hasanen A. Hammad

doi:10.3934/math.20251068

AIMS Mathematics

2025, Volume 10, Issue 10: 24061-24092. doi: 10.3934/math.20251068

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Research article

Investigating positive solutions in $ p $-Laplacian fractional systems with infinite-point boundaries

Doha A. Kattan ¹,
Hasanen A. Hammad ^{2,3
,
,}

1.
Department of Mathematics, College of Sciences and Art, King Abdulaziz University, Rabigh, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt

Received: 15 July 2025 Revised: 10 October 2025 Accepted: 16 October 2025 Published: 21 October 2025
MSC : 34A08, 34B15, 30C45, 47H10

This study explored the theoretical characteristics of a $ p $-Laplacian fractional-order differential equation. This equation was subject to both infinite-point boundary value requirements and nonlocal integral value constraints. We began by examining the associated Green's function, deriving its explicit expression and unique properties. These properties were then utilized to establish the existence and uniqueness of positive solutions through the application of the Banach fixed-point technique. Furthermore, we employed the nonlinear alternative of Leray-Schauder type, specifically Guo-Krasnoselskii's fixed-point theorem on cones, to demonstrate existence results for cases where the nonlinearity exhibits singularity with respect to the time variable. The practical relevance and applicability of our findings were illustrated through compelling examples. This research significantly contributed to the field of fractional differential equations, particularly within the domain of $ p $-Laplacian Hadamard fractional differential equations.
- nonlinear equation,
- $ p $-Laplacian fractional operator,
- existence result,
- fixed point methodology,
- singular nonlinear term,
- fractional derivative
Citation: Doha A. Kattan, Hasanen A. Hammad. Investigating positive solutions in $ p $-Laplacian fractional systems with infinite-point boundaries[J]. AIMS Mathematics, 2025, 10(10): 24061-24092. doi: 10.3934/math.20251068

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Abstract

This study explored the theoretical characteristics of a $ p $-Laplacian fractional-order differential equation. This equation was subject to both infinite-point boundary value requirements and nonlocal integral value constraints. We began by examining the associated Green's function, deriving its explicit expression and unique properties. These properties were then utilized to establish the existence and uniqueness of positive solutions through the application of the Banach fixed-point technique. Furthermore, we employed the nonlinear alternative of Leray-Schauder type, specifically Guo-Krasnoselskii's fixed-point theorem on cones, to demonstrate existence results for cases where the nonlinearity exhibits singularity with respect to the time variable. The practical relevance and applicability of our findings were illustrated through compelling examples. This research significantly contributed to the field of fractional differential equations, particularly within the domain of $ p $-Laplacian Hadamard fractional differential equations.

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