A robust study on fractional order HIV/AIDS model by using numerical methods.

Purpose: The fractional order HIV model has an important role in biological science. To study the HIV model in a better way, the model is presented with the help of Atangana- Baleanu operator which is in Caputo sense. Also, the characteristics of the solutions are described briefly with the help of the advance numerical techniques for the different values of fractional order derivatives. This paper aims to discuss the aforementioned objectives. Design/methodology/approach: In this work, Adams-Bashforth method and Euler method are used to get the solution of the HIV model. These are the important numerical methods. The comparison results also are described with the physical meaning of the solutions of the model. Findings: HIV model is analyzed under the view of fractional and AB derivative in Atangana-Baleanu-Caputo sense. The uniqueness of the solution is proved by using Banach Fixed point. The solution is derived with the help of Sumudu transform. Further, the authors employed fractional Adam-Bashforth method and Euler method to enumerate numerical results. The authors have used several values of fractional orders to present the outcomes graphically. The above calculations have been done with the help of MATLAB (R2016a). The numerical scheme used in the proposed study is valid and fruitful, and the same can be used to explore other real issues. Research limitations/implications: This investigation can be done for the real data sets. Practical implications: This paper aims to express the solution of the HIV model in a better way with the effect of non-locality, this work is very useful. Originality/value: In this work, HIV model is developed with the help of Atangana- Baleanu operator in Caputo sense. By using Banach Fixed point, the authors proved that the solution is unique. Also, the solution is presented with the help of Sumudu transform. The behaviors of the solutions are checked for different values of fractional order derivatives with the physical meaning with help of the Adam-Bashforth method and the Euler method. [ABSTRACT FROM AUTHOR]