Fractal dynamics of solution moments for the KPP–Fisher equation

Abstract

The paper focuses on the KPP–Fisher equation (named after Andrey Kolmogorov, Ivan Petrovskii, Nikolai Piskunov and Ronald Fisher) with non-local competitive losses and fractal time derivative which is considered in terms of F^α-calculus on the Cantor set dimension 0 < α < 1. A dynamic system with the fractal time derivative relating to the moments not higher than the second-order for the KPP–Fisher equation, is deduced in the semiclassical approximation with respect to the small diffusion parameter in the class of trajectory-concentrated functions. An example is given to the dynamic system of solution moments constructed and explored for various values of α parameter.