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, 2025)
This paper investigates a novel nonlinear singular fractional SI model withthe $Φ_p$ operator and the Mittag-Leffler kernel. The initial investigation includes theexistence, uniqueness, boundedness, and non-negativity of the solution. We thenestablish Hyers-Ulam stability for the proposed model in Banach space. Optimalcontrol analysis is performed to minimize the spread of infection and maximize thepopulation of susceptible individuals. Finally, the theoretical results are supportedby numerical simulations.