On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative

Abstract

In our research article, the mathematical model of fractional non-linear cancer dynamical system with the interaction of tumor cells, immune, and drugs reaction systems is taken in $\mathcal{ABC}$ derivative sense of fractional order. Qualitative results including existence and uniqueness has been analyzed by applying some theorems of fixed point theory. The approximate results for the considered system are obtained by numerical method due to Adams–Bashforth $\left(\mathcal{AB}\right)$ in non-integer order. Simulation of the Obtained iterative scheme are then drawn against the real data for different non-integer order. The suitability of the proposed model for our results are applied to study dynamics of tumor cells which help in investigating the dynamical interaction among tumor cells, immune cells and drugs reaction of the disease.