Diverse novel computational wave solutions of the time fractional Kolmogorov—Petrovskii - Piskunov and the (2 + 1)-dimensional Zoomeron equations

Abstract

The numerical wave solutions of two fractional biomathematical and statistical physics models (the Kolmogorov—Petrovskii - Piskunov (KPP) equation and the (2 + 1)-dimensional Zoomeron (Z) equation) are investigated in this manuscript. Many novel analytical solutions in different mathematical formulations such as trigonometric, hyperbolic, exponential, and so on can be constructed using the generalized Riccati—expansion analytical scheme and the Caputo—Fabrizio fractional derivative. The fractional nonlinear evolution equation is converted into an ordinary differential equation with an integer order using this fractional operator. The obtained solution is used to describe the transmission of a preferred allele and the nonlinear interaction of moving waves, and the relative wave mode’s amplitude dynamic. To illustrate the fractional examined models, several drawings are explained in two dimensions and density plots.