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Fractal Fract
Volume 9
Issue 2
10.3390/fractalfract9020092
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Qualitative Analysis of Generalized Power Nonlocal Fractional System with p-Laplacian Operator, Including Symmetric Cases: Application to a Hepatitis B Virus Model

by
Mohamed S. Algolam
1,
Mohammed A. Almalahi
2,
Muntasir Suhail
3,*,
Blgys Muflh
4,
Khaled Aldwoah
5,*,
Mohammed Hassan
6 and
Saeed Islam
7
1
Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
2
Department of Artificial Intelligence, College of Computer and Information Technology, Al-Razi University, Sana’a 12544, Yemen
3
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
4
Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
5
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
6
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
7
Department of Mechanical Engineering, Prince Muhammad Bin Fahad University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2025, 9(2), 92; https://doi.org/10.3390/fractalfract9020092 (registering DOI)
Submission received: 26 December 2024 / Revised: 26 January 2025 / Accepted: 29 January 2025 / Published: 1 February 2025
(This article belongs to the Special Issue Advanced Numerical Methods for Fractional Functional Models)
Versions Notes

Abstract

This paper introduces a novel framework for modeling nonlocal fractional system with a p-Laplacian operator under power nonlocal fractional derivatives (PFDs), a generalization encompassing established derivatives like Caputo–Fabrizio, Atangana–Baleanu, weighted Atangana–Baleanu, and weighted Hattaf. The core methodology involves employing a PFD with a tunable power parameter within a non-singular kernel, enabling a nuanced representation of memory effects not achievable with traditional fixed-kernel derivatives. This flexible framework is analyzed using fixed-point theory, rigorously establishing the existence and uniqueness of solutions for four symmetric cases under specific conditions. Furthermore, we demonstrate the Hyers–Ulam stability, confirming the robustness of these solutions against small perturbations. The versatility and generalizability of this framework is underscored by its application to an epidemiological model of transmission of Hepatitis B Virus (HBV) and numerical simulations for all four symmetric cases. This study presents findings in both theoretical and applied aspects of fractional calculus, introducing an alternative framework for modeling complex systems with memory processes, offering opportunities for more sophisticated and accurate models and new avenues for research in fractional calculus and its applications.
Keywords: p-Laplacian operator; power nonlocal kernels; fractional derivatives; mathematical model; stability; simulation p-Laplacian operator; power nonlocal kernels; fractional derivatives; mathematical model; stability; simulation

Share and Cite

MDPI and ACS Style

Algolam, M.S.; Almalahi, M.A.; Suhail, M.; Muflh, B.; Aldwoah, K.; Hassan, M.; Islam, S. Qualitative Analysis of Generalized Power Nonlocal Fractional System with p-Laplacian Operator, Including Symmetric Cases: Application to a Hepatitis B Virus Model. Fractal Fract. 2025, 9, 92. https://doi.org/10.3390/fractalfract9020092

AMA Style

Algolam MS, Almalahi MA, Suhail M, Muflh B, Aldwoah K, Hassan M, Islam S. Qualitative Analysis of Generalized Power Nonlocal Fractional System with p-Laplacian Operator, Including Symmetric Cases: Application to a Hepatitis B Virus Model. Fractal and Fractional. 2025; 9(2):92. https://doi.org/10.3390/fractalfract9020092

Chicago/Turabian Style

Algolam, Mohamed S., Mohammed A. Almalahi, Muntasir Suhail, Blgys Muflh, Khaled Aldwoah, Mohammed Hassan, and Saeed Islam. 2025. "Qualitative Analysis of Generalized Power Nonlocal Fractional System with p-Laplacian Operator, Including Symmetric Cases: Application to a Hepatitis B Virus Model" Fractal and Fractional 9, no. 2: 92. https://doi.org/10.3390/fractalfract9020092

APA Style

Algolam, M. S., Almalahi, M. A., Suhail, M., Muflh, B., Aldwoah, K., Hassan, M., & Islam, S. (2025). Qualitative Analysis of Generalized Power Nonlocal Fractional System with p-Laplacian Operator, Including Symmetric Cases: Application to a Hepatitis B Virus Model. Fractal and Fractional, 9(2), 92. https://doi.org/10.3390/fractalfract9020092

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