A Study on the Fractional Ebola Virus Model by the Semi-Analytic and Numerical Approach

Document Type : Research Paper

Authors

Department of Mathematics, Bangalore University, Bengaluru-560056, India.

Abstract

In this study, An Ebola virus model involving the fractional derivatives in the Caputo sense is considered and studied through three different techniques called the Homotopy analysis method (HAM), Haar wavelet method (HWM), and Runge-Kutta method (RKM). 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 RK method 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 HAM by choosing the preferred control parameter. Secondly, HWT is considered; through this technique, the operational matrix of integration is used to convert the given FDEs into a set of algebraic equation systems, and then the RK method 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. Theorems on convergence have been discussed in terms of theorems.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 August 2024

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History

  • Receive Date: 02 May 2024
  • Revise Date: 29 June 2024
  • Accept Date: 31 July 2024

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