Mathematical modeling for solving fractional model cancer bosom malignant growth - Shaimaa A. M. Abdelmohsen; D. Sh. Mohamed; Haifa A. Alyousef; M. R. Gorji; Amr M. S. Mahdy (AIMS Biophysics, 2023)
In this essay, we have presented a fractional numerical model of breast cancer stages with cardiac outcomes. Five compartments were used to build the model, each of which represented a subpopulation of breast cancer patients. Variables A, B, C, D, and E each represent a certain subpopulation. They are levels 1 and 2 (A), level 3 (B), level 4 (C), disease-free (D) and cardiotoxic (E). We have demonstrated that the fractional model has a stable solution. We also discuss how to optimally control this model and numerically simulate the control problem. Using numerical simulations, we computed the results of the dissection. The model's compartment diagram has been completed. A predictor-corrector method has been used to manage the fractional derivatives and produce numerical solutions. The Caputo sense has been used to describe fractional derivatives. The results have been illustrated through numerical simulations. Furthermore, the numerical simulations show that the cancer breast malignant growth fractional order model is easier to model than the traditional integer-order model. To compute the results, we have used mathematical programming. We have made it clear that the numerical method that was applied in this publication to solve this model was not utilized by any other author before that, nor has this method been investigated in the past. Our investigation established this approach.