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 orterminating myelogenous leukemia blood cancer s cells against naive T-celland e ective T-cell population of body, presented by fractional di erentialequations. We use this model to analyze the stability of the dynamics, whichoccur in the local interaction of e ector-immune cell and tumor cells. Wewill also investigate the optimal control of combined chemo-immunotherapy.We claim that our fractional di erential equations model is superior to itsordinary di erential equations counterpart in facilitating understanding of thenatural immune interactions to tumor and of the detrimental side e ects whichchemotherapy may have on a patient s immune system.

Keywords:

Fractional di erential equations , Stability , Myelogenous leukemia blood cancer