grunwald-letnikov scheme for system of chronic myelogenous leukemia fractional differential equations and its optimal control of drug treatment

In this article, a mathematical model describing the growth or terminating myelogenous leukemia blood cancer's cells against naive t-cell and e ective t-cell population of body, presented by fractional di erential equations. we use this model to analyze the stability of the dynamics, which occur in the local interaction of e ector-immune cell and tumor cells. we will also investigate the optimal control of combined chemo-immunotherapy. we claim that our fractional di erential equations model is superior to its ordinary di erential equations counterpart in facilitating understanding of the natural immune interactions to tumor and of the detrimental side e ects which chemotherapy may have on a patient's immune system.