A study on the fractional Ebola virus model by the semi-analytic and numerical approach

In this study, an Ebola virus model involving fractional derivatives in the Caputo sense is considered and studied through three different techniques called the homotopy analysis method (HAM), the Haar wavelet method (HWM), and the Range-Kutta method (RKM). The HAM is a semi-analytical approach proposed for solving fractional-order nonlinear systems of ordinary differential equations (ODEs), the Haar wavelet technique (HWT) is a numerical approach for both fractional and integer order, and the RKM is a numerical method used to solve the system of ODEs. We have drawn a semi-analytical solution in terms of a series of polynomials and numerical solutions for the model. First, we solved the model through the HAM by choosing the preferred control parameter. Secondly, the HWT is considered; through this technique, the operational matrix of integration is used to convert the given fractional differential equations (FDEs) into a set of algebraic equation systems, and then the RKM is applied. The model is studied through all three methods, and the solutions are juxtaposed with ND Solver solutions. The nature of the model is analyzed with different parameters, and the calculations are performed using Scilab and Mathematica software. The obtained results are expressed in graphs and tables. Convergence analysis has been discussed in terms of theorems.

کلیدواژه ها:

fractional calculus ، Ebola virus model ، homotopy analysis method ، Haar wavelet