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Volume 17, Issue 5
Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with $Φ_p$ Operator and Mittag-Leffler Kernel

Achraf Zinihi, Moulay Rchid Sidi Ammi & Matthias Ehrhardt

DOI: 10.4208/aamm.OA-2024-0134

Adv. Appl. Math. Mech., 17 (2025), pp. 1481-1508.

Published online: 2025-07

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  • Abstract

This paper investigates a novel nonlinear singular fractional SI model with the $Φ_p$ operator and the Mittag-Leffler kernel. The initial investigation includes the existence, uniqueness, boundedness, and non-negativity of the solution. We then establish Hyers-Ulam stability for the proposed model in Banach space. Optimal control analysis is performed to minimize the spread of infection and maximize the population of susceptible individuals. Finally, the theoretical results are supported by numerical simulations.

  • Keywords

Epidemiological model, fractional differential equations, $p$-Laplacian operator, numerical approximations, optimal control.

  • AMS Subject Headings

92C60, 34A08, 47H20, 33F05, 49J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-17-1481, author = {Zinihi , AchrafAmmi , Moulay Rchid Sidi and Ehrhardt , Matthias}, title = {Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with $Φ_p$ Operator and Mittag-Leffler Kernel}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {5}, pages = {1481--1508}, abstract = {

This paper investigates a novel nonlinear singular fractional SI model with the $Φ_p$ operator and the Mittag-Leffler kernel. The initial investigation includes the existence, uniqueness, boundedness, and non-negativity of the solution. We then establish Hyers-Ulam stability for the proposed model in Banach space. Optimal control analysis is performed to minimize the spread of infection and maximize the population of susceptible individuals. Finally, the theoretical results are supported by numerical simulations.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2024-0134}, url = {http://global-sci.org/intro/article_detail/aamm/24289.html} }
TY - JOUR T1 - Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with $Φ_p$ Operator and Mittag-Leffler Kernel AU - Zinihi , Achraf AU - Ammi , Moulay Rchid Sidi AU - Ehrhardt , Matthias JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1481 EP - 1508 PY - 2025 DA - 2025/07 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2024-0134 UR - https://global-sci.org/intro/article_detail/aamm/24289.html KW - Epidemiological model, fractional differential equations, $p$-Laplacian operator, numerical approximations, optimal control. AB -

This paper investigates a novel nonlinear singular fractional SI model with the $Φ_p$ operator and the Mittag-Leffler kernel. The initial investigation includes the existence, uniqueness, boundedness, and non-negativity of the solution. We then establish Hyers-Ulam stability for the proposed model in Banach space. Optimal control analysis is performed to minimize the spread of infection and maximize the population of susceptible individuals. Finally, the theoretical results are supported by numerical simulations.

Zinihi , AchrafAmmi , Moulay Rchid Sidi and Ehrhardt , Matthias. (2025). Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with $Φ_p$ Operator and Mittag-Leffler Kernel. Advances in Applied Mathematics and Mechanics. 17 (5). 1481-1508. doi:10.4208/aamm.OA-2024-0134
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