Ali F.  Jameel, Majid M.  Hamed, N.R.  Anakira, A.  Saaban, Farah A.  Abdullah, 
    Numerical Treatment of Fractional Tumor Immune System Model by
Adam-Bashforth Moulton Method,
    Journal of Engineering and Applied Sciences,
    Volume 14,Issue 2,
    2019,
    Pages 495-501,
    ISSN 1816-949x,
    jeasci.2019.495.501,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2019.495.501)
    Abstract: In this study, the fractional order of tumor cell growth and their interactions with effectors such as
cytotoxic T-cells, E<sub>1</sub>(t) and natural killer cells E<sub>2</sub>(t) are studied. The Adam-Bashforth-Moulton algorithm is used 1 2
to numerically solve and simulate the model of the tumor immune system with fractional order. From the
observation of the numerical result, reduces &alpha; from 1-0.75, decrease the maximum of tumor cells. Numerical
simulations illustrate that the fractional-order derivative enriches the dynamics of the system and increases the
complexity of the observed behaviors which confirms that the fractional-order may play the role of memory in
the system.
    Keywords: Fractional calculus;Adam-Bashforth-Moulton method;tumor-immune system;illustrate;memory;numerical simulations