# On the Numerical Method for Solving a System of Nonlinear Fractional Ordinary Differential Equations Arising in HIV Infection of CD4$$^{+}$$ T Cells

• Farshid Mirzaee
Research Paper

## Abstract

In this study, shifted Legendre collocation method is used to provide an approximate solution of a fractional order model of HIV infection of CD4$$^{+}$$ T cells. This model corresponds to a nonlinear system of fractional ordinary differential equation. By using the present method, the solution of this nonlinear system converts to the solution of nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. Furthermore, convergence and error analysis of the proposed method are discussed and an upper error bound is provided under weak assumptions. Finally, numerical results for solving fractional model of HIV infection of CD4$$^{+}$$ T cells with various parameters are reported in tables. Also, we survey the effect of changing the parameter $$\alpha$$ on the present model.

## Keywords

A model of HIV infection of CD4$$^{+}$$ T cells Fractional derivatives Shifted Legendre collocation method Nonlinear system of differential equations Convergence analysis

## Mathematics Subject Classification

26A33 35A24 33C45 65L70

## Notes

### Acknowledgements

The authors would like to express our very great appreciation to reviewers for their valuable comments and suggestions which have helped to improve the quality and presentation of this paper.

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