Numerical Simulation of the Fractal-Fractional Ebola Virus

Fractal and Fractional

H.M. Srivastava¹  KhaledM. Saad² 

[1] Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Mathematics, College of Sciences and Arts, Najran University, Najran P.O. Box 1988, Saudi Arabia;

关键词: fractal-fractional ebola virus;    lagrange polynomial interpolation;    power law;    exponential law;    generalized mittag-leffler function;   

DOI  :  10.3390/fractalfract4040049

来源: DOAJ

【 摘 要 】

In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the generalized Mittag-Leffler function by using the concepts of the fractal differentiation and fractional differentiation. These operators have two parameters: The first parameter $\rho$ is considered as the fractal dimension and the second parameter k is the fractional order. We evaluate the numerical solutions of the fractal-fractional Ebola virus for these operators with the theory of fractional calculus and the help of the Lagrange polynomial functions. In the case of $\rho =k=1$, all of the numerical solutions based on the power kernel, the exponential kernel and the generalized Mittag-Leffler kernel are found to be close to each other and, therefore, one of the kernels is compared with such numerical methods as the finite difference methods. This has led to an excellent agreement. For the effect of fractal-fractional on the behavior, we study the numerical solutions for different values of $\rho$ and $k.$ All calculations in this work are accomplished by using the Mathematica package.

【 授权许可】

Unknown