Abstract This paper proposes the notion of a fractional generalised integral transform (Fractional G -transform) using modified Riemann-Liouville derivative with the Mittag-Leffler function as a kernel. We investigate the basic properties of the Fractional G -transform. In addition, the homotopy analysis is incorporated to introduce a hybrid Fractional Generalised Homotopy Analysis Method using Modified Riemann-Liouville Derivative, which is denoted as MRFGHAM. We highlight the merits of MRFGHAM and apply it to solve fractional nonlinear differential equations. The proposed method is implemented to formulate a fractional non-fatal disease epidemic model and to obtain the results of a spreading process subject to various settings of the fractional parameters. We also statistically validate the variations in the spread of the non-fatal disease obtained at different stages. Furthermore, the fractional power epidemic model is reduced to a simple epidemic model, and the obtained results indicate an excellent agreement with those of existing conventional methods.

中文翻译：

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使用修正黎曼-刘维尔导数的分数广义同伦分析法分析分数流行病模型

摘要 本文提出了以 Mittag-Leffler 函数为核的修正 Riemann-Liouville 导数的分数阶广义积分变换 (Fractional G -transform) 的概念。我们研究了分数 G 变换的基本性质。此外，还引入了同伦分析，引入了一种使用修正黎曼-刘维尔导数的混合分数广义同伦分析方法，记为 MRFGHAM。我们强调了 MRFGHAM 的优点并将其应用于求解分数阶非线性微分方程。实施所提出的方法以制定分数非致命疾病流行模型并获得受分数参数的各种设置影响的传播过程的结果。我们还统计验证了在不同阶段获得的非致命疾病传播的变化。此外，将分数幂流行模型简化为简单的流行模型，所得结果与现有常规方法的结果非常吻合。