Abstract
We implement relatively new analytical technique, the Homotopy perturbation method, for solving nonlinear fractional partial differential equations arising in predator-prey biological population dynamics system. Numerical solutions are given, and some properties exhibit biologically reasonable dependence on the parameter values. And the fractional derivatives are described in the Caputo sense.
Highlights
It has turned out that many phenomena in engineering, physics, chemistry, other sciences 1–3 can be described very successfully by models using mathematical tools form fractional calculus, such as anomalous transport in disordered systems, some percolations in porous media, and the diffusion of biological populations
The application of the method is extended for fractional differential equations 13–15
According to a widely accepted knowledge of fractional calculus and biological population, the time-fractional dynamics of a predator-prey system can be described by the equations
Summary
It has turned out that many phenomena in engineering, physics, chemistry, other sciences 1–3 can be described very successfully by models using mathematical tools form fractional calculus, such as anomalous transport in disordered systems, some percolations in porous media, and the diffusion of biological populations. The Homotopy Perturbation Method HPM is relatively new approach to provide an analytical approximation to nonlinear problem. This method was first presented by He 8, 9 and applied to various nonlinear problems 10–12. Kadem and Baleanu 23 studied the coupled fractional Lotka-Volterra equations using the Homotopy perturbation method. According to a widely accepted knowledge of fractional calculus and biological population, the time-fractional dynamics of a predator-prey system can be described by the equations. We consider the fractional nonlinear predator-prey population model.
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