Extremal and uniqueness results for a singular p-Laplacian Caputo-Hadamard fractional equation involving parameter dependence
- 1School of Sciences, Changzhou Institute of Technology, Changzhou213002, Jiangsu, China
Abstract
Owing to the non-ideal properties of the Green’s function associated with the boundary value problem of Caputo-Hadamard fractional differential equations, a complete theoretical framework for studying such solutions has remained elusive. To address this challenge, this paper introduces novel substitutions and conducts a meticulous analysis of the Green’s function’s properties. This approach enables us to successfully derive the maximum and minimum iterative solutions for a singular p-Laplacian Caputo-Hadamard fractional differential equation. Subsequently, by employing the theory of mixed monotone operators, we establish the existence and uniqueness of positive solutions. Furthermore, we demonstrate that the unique solution uλ⋆ uλ ⋆ is parameter-dependent, exhibiting the asymptotic behavior limλ→∞‖uλ⋆‖=0 limλ → ∞ ‖uλ ⋆ ‖=0 and limλ→0+‖uλ⋆‖=∞ ${\mathrm{lim}}_{\lambda \to {0}^{+}}{\Vert}{u}_{\lambda }^{\star }{\Vert}=\infty $ . The validity of our main theoretical findings is confirmed through a numerical example, with graphical illustrations depicting the solution’s variation with the parameter.
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BibTeX
@article{limin2026extremal,
title = {{Extremal and uniqueness results for a singular p-Laplacian Caputo-Hadamard fractional equation involving parameter dependence}},
author = {Guo Limin},
journal = {Demonstratio Mathematica},
year = {2026},
month = oct,
doi = {10.1515/dema-2025-0320},
url = {https://doi.org/10.1515/dema-2025-0320},
note = {CC BY},
}
RIS
TY - JOUR
TI - Extremal and uniqueness results for a singular p-Laplacian Caputo-Hadamard fractional equation involving parameter dependence
AU - Guo Limin
PY - 2026
DA - 2026/10/26
JO - Demonstratio Mathematica
DO - 10.1515/dema-2025-0320
UR - https://doi.org/10.1515/dema-2025-0320
AB - Owing to the non-ideal properties of the Green’s function associated with the boundary value problem of Caputo-Hadamard fractional differential equations, a complete theoretical framework for studying such solutions has remained elusive. To address this challenge, this paper introduces novel substitutions and conducts a meticulous analysis of the Green’s function’s properties. This approach enables us to successfully derive the maximum and minimum iterative solutions for a singular p-Laplacian Caputo-Hadamard fractional differential equation. Subsequently, by employing the theory of mixed monotone operators, we establish the existence and uniqueness of positive solutions. Furthermore, we demonstrate that the unique solution uλ⋆ u_λ ^⋆ is parameter-dependent, exhibiting the asymptotic behavior limλ→∞‖uλ⋆‖=0 lim_λ → ∞ ‖u_λ ^⋆ ‖=0 and limλ→0+‖uλ⋆‖=∞ ${\mathrm{lim}}_{\lambda \to {0}^{+}}{\Vert}{u}_{\lambda }^{\star }{\Vert}=\infty $ . The validity of our main theoretical findings is confirmed through a numerical example, with graphical illustrations depicting the solution’s variation with the parameter.
SN - 2391-4661
ER -