A vitamin intervention study on the tumour and immune cells via TIV dynamical system-revisited

Abstract

This paper presents wavelet and other numerical techniques for solving systems of tumour-immune-vitamin intervention (TIV) model with non-integer order and nonlinear. For the first time, fractional order TIV system has been solved by using Bernstein wavelet collocation method (BWCM). This process uses wavelet approximations depend on Bernstein wavelets and their non-integer integral to transform non-integer differential systems into algebraic equation. This fractional TIV model will represent the effects of memory on the system. Three elements make up this partial sequence TIV system: vitamin intervention, immune cells, and tumour cells. Boundedness and non-negativity, residual error and convergence analysis of solutions have been determined using the iterative approach and BWCM. This investigation shows that the technique is very much useful and efficient for TIV intervention. Also, we have discussed the existence and uniqueness of the non-integer order TIV model. According to the findings, the TIV system would benefit from the use of the BWCM and this numerical method will open more research. Our findings will be valuable to biologists and researcher in the treatment of TIV.

Keywords

• Fractional order model
• Bernstein wavelet collocation method
• operational matrix
• numerical method
• existence and uniqueness
• positivity and boundedness