El-Sayed, A. M. A.; Rida, S. Z.; Arafa, A. A. M. Exact solutions of fractional-order biological population model. (English) Zbl 1184.92038 Commun. Theor. Phys. 52, No. 6, 992-996 (2009). Summary: The 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 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. Cited in 52 Documents MSC: 92D25 Population dynamics (general) 35Q92 PDEs in connection with biology, chemistry and other natural sciences 28A80 Fractals 35K57 Reaction-diffusion equations 37F99 Dynamical systems over complex numbers Keywords:biological population model; fractional calculus; decomposition method; Mittag-Leffler function Citations:Zbl 0671.34053; Zbl 0882.34007 PDFBibTeX XMLCite \textit{A. M. A. El-Sayed} et al., Commun. Theor. Phys. 52, No. 6, 992--996 (2009; Zbl 1184.92038) Full Text: DOI