New Fractional Cancer Mathematical Model via IL-10 Cytokine and Anti-PD-L1 Inhibitor

In this study, we explore a recent biological model created to analyze the behavior of cancer cells by administering a dose of a drug containing anti-PD-L1 and IL-10 with the Caputo and Atangana–Baleanu derivative in the Caputo sense (ABC). Using the Caputo derivative in order to examine the stability of the non-linear system, we are able to demonstrate that it is existent and unique, and to introduce several numeric data obtained for the fractional values in MATLAB by using the Adams–Bashforth–Moulton (ABM) method. Additionally, by using the predictor–corrector approach, the numerical results from the system with ABC derivative will be produced. As a result, it has been observed that immune system cells that are exposed to single-dose drug with fractional order effectively combat cancer cells. The tumor cells decrease by $70.44\%$ and $80.16\%$ for the system generalized by the Caputo and ABC derivative, respectively, for the order $\alpha =0.42$.