A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative. (April 2020) - Ghanbari, Behzad; Kumar, Sunil; Kumar, Ranbir
Highlights: A new immunogenetic tumour model with non-singular fractional derivative is considered. A new derivative Atangana-Baleanu derivative is considered. The Adam Bashforths Moulton method will then be used to solve this fractional immunogenetic tumour model. The convergence and uniqueness of the immunogenetic tumour model are presented. Abstract: Mathematical biology is one of the interesting research area of applied mathematics that describes the accurate description of phenomena in biology and related health issues. The use of new mathematical tools and definitions in this area of research will have a great impact on improving community health by controlling some diseases. This is the best reason for doing new research using the latest tools available to us. In this work, we will make novel numerical approaches to the immunogenetic tumour model to using differential and integral operators with Mittag-Leffler law. To be more precise, the fractional Atangana- Baleanu derivative has been utilized in the structure of proposed model. This paper proceeds by examining and proving the convergence and uniqueness of the solution of these equations. The Adam Bashforth's Moulton method will then be used to solve proposed fractional immunogenetic tumour model. Numerical simulations for the model are obtained to verify the applicability and computational efficiency of the considered process. Similar models in this field can also be explored similarly to what has been done in this article.