Controllability and analysis of sustainable approach for cancer treatment with chemotherapy by using the fractional operator

This research proposes a mathematical model of cancer treatment with chemotherapy using a fractal fractional Mittag-Leffler operator with non-integer order. The model is analyzed both qualitatively and quantitatively. The control of cancer treatment with chemotherapy effects is established using a fractal fractional operator with a Mittag-Leffler kernel and control theory. The effect of global derivative, existence of unique solutions, and boundedness of proposed system is verified. Solutions are produced using a two-step Lagrange polynomial, and numerical simulations are carried out to illustrate the theoretical results. Cancer treatment with chemotherapy effects are verified from our justified results and predictions are made by simulation using MATLAB. Controllability and observability of the proposed system is also treated for linear control system to observe the close loop design with chemotherapy as an input and treated cells as the output