Fractional mathematical model underlying mixed treatments using endocrine diet therapy and immunotherapy for breast cancer

. To understand cancer as a biomathematical process, we establish our model to give an analytical and a numerical examination of the fractional derivative impact on developing breast cancer with endocrine diet therapy and immunotherapy. So, we try, in this paper, to formulate the cancer dynamics involving the normal cells, tumor cells, immune cells, estrogen (endocrine parameter) and immunotherapy. We show the wellposedness of the breast cancer model and we analyze the existence and the stability of the equilibria, then, we discuss the numerical results in order to conclude that the use of fractional derivatives provides more useful information about the stability of the breast cancer dynamics with mixed treatments model.