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 - <p style="text-align: justify;">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.</p>