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Zbl 1105.65122
Ahmed, E.; El-Sayed, A.M.A.; El-Saka, H.A.A.
Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. (English)
[J] J. Math. Anal. Appl. 325, No. 1, 542-553 (2007). ISSN 0022-247X

Summary: We are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

MSC 2000:: *65R20 Integral equations (numerical methods)
92D30 Epidemiology
45J05 Integro-ordinary differential equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: predator-prey system; rabies system; fractional-order differential equations; equilibrium points; stability; predictor-corrector method; numerical examples

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Zentralblatt MATH Berlin [Germany]