Analysis of a fractional epidemic model by fractional generalised homotopy analysis method using modified Riemann - Liouville derivative

摘要

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.