In this paper, Generalized Mittag-Leffler function method (GMLFM) and Sumudu transform method (STM) are applied to study and solve the fractional order smoking model, where the derivatives are defined in the Caputo fractional sense. The disease free equilibrium (DFE) and stability of equilibrium point are studied. Lyapunov exponents and Poincare map of the model are drawn to ensure the stability of the model. The obtained results show that the proposed methods are very effective and convenient. In addition, the model is presented by its signal flow graph and simulated using Matlab/Simulink.

中文翻译：

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求解非线性分数阶吸烟模型的近似解

本文采用广义Mittag-Leffler函数方法（GMLFM）和Sumudu变换方法（STM）来研究和求解分数阶吸烟模型，其中以Caputo分数意义定义了导数。研究了无病平衡和平衡点的稳定性。绘制了模型的Lyapunov指数和Poincare图，以确保模型的稳定性。所得结果表明，所提出的方法是非常有效和方便的。此外，该模型由其信号流图表示，并使用Matlab / Simulink进行仿真。