solving the fractional hiv model using bell polynomials and the tau method

This paper introduces a tau-based numerical approach utilizing bell polynomials to solve a fractional hiv model involvingcd4 +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 l² [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.