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A fractional diffusion equation model for cancer tumor
1.S. M. Ali, A. H. Bokhari, M. Yousuf, and F. D. Zaman, “A spherically symmetric model for the tumor growth,” Journal of Applied Mathematics art. no. 726837 (2014).
2.S. Benzekry, C. Lamont, A. Beheshti, A. Tracz, and JML Ebos et al., “Classical mathematical models for description and prediction of experimental tumor growth,” PLOS Computational Biology 10(8), e1003800 (2014).
3.A. H. Bokhari, A. H. Kara, and F. D. Zaman, “On the solutions and conservation laws of the model for tumor growth in the brain,” Journal of Mathematical Analysis and Applications 350, 256–261 (2009).
4.P. K. Burgess, P. M. Kulesa, J. D. Murray, and E. C. Alroid, “The interaction of growth rates and diffusion coefficients in a three dimensional mathematical model of gliomas,” Journal of Neuropath Exp. Neur. 56, 704–713 (1997).
6.E. Cumberbatch and A. Fitt, Mathematical Modeling: Case Studies from Industries (Cambridge University Press, UK, 2001).
7.M. A. El-Tawil and S. N. Huseen, “The Q-Homotopy Analysis Method (Q-HAM),” Int. J. of Appl. Math. and Mech. 8(15), 51–75 (2012).
8.A. Iomin, “Superdiffusion of cancer on a comb structure,” Journal of Physics: Conference Series 7, 57–67 (2005).
9.O. S. Iyiola, “A numerical study of ito equation and sawada-kotera equation both of time-fractional type,” Adv. Math: Sci Journal 2(2), 71–79 (2013).
10.O. S. Iyiola, M. E. Soh, and C. D. Enyi, “Generalised homotopy analysis method (q-HAM) for solving foam drainage equation of time fractional type,” Math. in Engr, Science and Aerospace 4(4), 105–116 (2013).
11.O. S. Iyiola and G. O. Ojo, “Analytical solutions of time-fractional models for homogeneous gardner equation and non-homogeneous differential equations,” Ain Shams Engineering Journal 5, 999–1004 (2014).
12.T. D. Laajala, J. Corander, N. M. Saarinen, K. Makela, S. Savolainen, M. I. Suominen, E. Alhoniemi, S. Makela, M. Poutanen, and T. Aittokallio, “Improved statistical modeling of tumor growth and treatment effect in preclinical animal studies with highly heterogeneous responses in vivo,” Clin Cancer Res. 18(16), 4385–4396 (2012).
14.G. I. Marchuk, Mathematical Models in Environmental Problems (North-Holland, Elsevier Science Publisher, 1986).
15.K. S. Miller and B. Ross, An Introduction to the fractional calculus and fractional differential equations (John Wiley and Sons, Inc, New York, 2003).
16.S. Moyo and P. G. L. Leach, “Symmetry methods applied to a mathematical model of a tumour of the brain,” Proceedings of Institute of Mathematics of NAS of Ukraine 50(1), 204–210 (2004).
17.E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow, Second ed. (Cambridge University Press, UK, 2001).
18.I. Podlubny, “Fractional Differential Equations,” Mathematics in Science and Engineering (Academic Press, San Diego, Calif, USA, 1999), Vol. 198.
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In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to the classical first order derivative in time. Three different cases of the net killing rate are taken into account including the case where net killing rate of the cancer cells is dependent on the concentration of the cells. At first, we use a relatively new analytical technique called q-Homotopy Analysis Method on the resulting time-fractional partial differential equations to obtain analytical solution in form of convergent series with easily computable components. Our numerical analysis enables us to give some recommendations on the appropriate order (fractional) of derivative in time to be used in modeling cancer tumor.
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