Одномерное уравнение Фишера-Колмогорова-Петровского-Пискунова с нелокальной нелинейностью и аномальной диффузией

Abstract

Analytical solutions are constructed for the nonlocal space fractional Fisher-Kolmogorov-Petrovskii-Piskunov equation with abnormal diffusion. Such solutions allow us to describe quasi-steady state patterns. Special attention is given to the role of fractional derivative. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fractional derivative used. Results of numerical simulations and properties of analytical solutions are presented. Influence of the fractional derivative on patterns ordered in space and time is discussed.