Solving the Fractional HIV Model using Bell Polynomials and the Tau Method

Document Type : Research Article

Authors

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, 35195-363, Semnan, Iran

Abstract

This paper introduces a Tau-based numerical approach utilizing Bell polynomials to solve a fractional HIV model involving $CD4^+ T$ cells. The model comprises a system of three fractional nonlinear ordinary differential equations. The method begins with deriving the operational matrix for the fractional derivative of Bell polynomials. Next, any function within the space \(L^2[0,1]\) is approximated using Bell polynomials, and these approximations are substituted into the model equations. The resulting expressions are used to compute Chebyshev collocation points within the interval \([0,1]\). By applying the Tau method along with the boundary conditions, the problem is converted into a system of algebraic equations that can be solved using standard numerical techniques such as Newton's method. An example is provided to illustrate the accuracy and effectiveness of the proposed method.

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References

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 1
May 2024
Pages 65-73

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History

  • Receive Date: 30 April 2025
  • Revise Date: 18 May 2025
  • Accept Date: 20 May 2025
  • Publish Date: 01 June 2025

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