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Zbl 1184.92038
El-Sayed, A.M.A.; Rida, S.Z.; Arafa, A.A.M.
Exact solutions of fractional-order biological population model. (English)
[J] Commun. Theor. Phys. 52, No. 6, Article ID 992 (2009). ISSN 0253-6102

Summary: The {\it G. Adomian}'s decomposition method (ADM) [J. Math. Anal. Appl. 135, No.~2, 501--544 (1988; Zbl 0671.34053)] is presented for finding the exact solutions of more general biological population models. A new solution is constructed by power series. The fractional derivatives are described in the {\it M. Caputo} sense [Ann. Univ. Ferrara, Nuova Ser., Sez. VII 41, 73--84 (1995; Zbl 0882.34007)]. To illustrate the reliability of the method, some examples are provided.

MSC 2000:: *92D25 Population dynamics
35Q92
28A80 Fractals
35K57 Reaction-diffusion equations
37F99 Complex dynamical systems

Keywords: biological population model; fractional calculus; decomposition method; Mittag-Leffler function

Citations: Zbl 0671.34053; Zbl 0882.34007

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Zentralblatt MATH Berlin [Germany]