Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. (English) Zbl 1105.65122

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

J. Math. Anal. Appl. 325, No. 1, 542-553 (2007).

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:

65R20	Numerical methods for integral equations
92D30	Epidemiology
45J05	Integro-ordinary differential equations
26A33	Fractional derivatives and integrals

Keywords:

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

Software:

FracPECE

References:

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