Extremal and uniqueness results for a singular p -Laplacian Caputo-Hadamard fractional equation involving parameter dependence
Year: 2026
Type: article
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 u λ ⋆ ${u}_{\lambda }^{\star }$ is parameter-dependent, exhibiting the asymptotic behavior lim λ → ∞ ‖ u λ ⋆ ‖ = 0 ${\mathrm{lim}}_{\lambda \to \infty }{\Vert}{u}_{\lambda }^{\star }{\Vert}=0$ and lim λ → 0 + ‖ u λ ⋆ ‖ = ∞ ${\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.
Source: Demonstratio Mathematica
Author: Limin Guo
Institution: Changzhou Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W7223242672