AN ANALYTICAL APPROACH TO THE FRACTIONAL BIOLOGICAL POPULATION MODEL VIA EXPONENTIAL LAW AND MITTAG-LEFFLER KERNEL

In this article, analytical approximate solution of time fractional non-linear biological population model which arises as a result of spatial diffusion is proposed. Considering the fractional derivatives in Atangana-Baleanu-Caputo and Caputo-FabrizioCaputo sense, the Laplace transform technique has been employed in combination to the homotopy perturbation method. Examples corresponding to Malthusian and Verhulst laws are worked out and it is shown that in most of the cases the numerical solution converges to the exact solution. The numerical simulations are presented to depict the behavior of the solution corresponding to the variations in the fractional parameter and time.