标题： 数学建模与非线性流行病学模型的Hyers-Ulam稳定性分析，带有$Φ_p$算子和Mittag-Leffler核 显示英文标题

标题： Mathematical Modeling and Hyers-Ulam Stability for a Nonlinear Epidemiological Model with $Φ_p$ Operator and Mittag-Leffler Kernel

摘要： 本文研究了一个具有$\Phi_p$算子和Mittag-Leffler核的新型非线性奇异分数阶SI模型。 初步研究包括解的存在性、唯一性、有界性和非负性。 然后我们在巴拿赫空间中建立了所提出模型的Hyers-Ulam稳定性。 进行最优控制分析以最小化感染的传播并最大化易感个体的人口数量。 最后，理论结果通过数值模拟得到支持。 显示英文摘要

摘要： This paper investigates a novel nonlinear singular fractional SI model with the $\Phi_p$ 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.