A novel mathematical approach of COVID-19 with non-singular fractional derivative

Sachin Kumar; Jinde Cao; Mahmoud Abdel-Aty

doi:10.1016/j.chaos.2020.110048

A novel mathematical approach of COVID-19 with non-singular fractional derivative

Chaos Solitons Fractals. 2020 Oct:139:110048. doi: 10.1016/j.chaos.2020.110048. Epub 2020 Jul 1.

Authors

Sachin Kumar¹, Jinde Cao², Mahmoud Abdel-Aty³

Affiliations

¹ Department of Mathematics, Govt. M.G.M PG College, Itarsi 461111, India.
² School of Mathematics, Southeast University, Nanjing, China.
³ Department of Mathematics, Faculty of Sciences, Sohag University, Sohag 82524, Egypt.

Abstract

We analyze a proposition which considers new mathematical model of COVID-19 based on fractional ordinary differential equation. A non-singular fractional derivative with Mittag-Leffler kernel has been used and the numerical approximation formula of fractional derivative of function ${(t - a)}^{n}$ is obtained. A new operational matrix of fractional differentiation on domain [0, a], a ≥ 1, a ∈ N by using the extended Legendre polynomial on larger domain has been developed. It is shown that the new mathematical model of COVID-19 can be solved using Legendre collocation method. Also, the accuracy and validity of our developed operational matrix have been tested. Finally, we provide numerical evidence and theoretical arguments that our new model can estimate the output of the exposed, infected and asymptotic carrier with higher fidelity than the previous models, thereby motivating the use of the presented model as a standard tool for examining the effect of contact rate and transmissibility multiple on number of infected cases are depicted with graphs.

Keywords: COVID-19 virus; Fractional derivative with Mittag-Leffler kernel; Fractional mathematical model; Spectral method.