FRACTIONAL FISHER-KPP TYPE EQUATIONS ON STRATIFIED GROUPS.

Abstract

This work investigates the fractional space-time behavior of the Fisher-KPP equation with initial boundary values. Notably, fractional versions of Fisher-KPP equations describe complex phenomena in cases where the classical local approach is limited. In this work, we combine different techniques from fractional calculus and non-commutative analysis, which provide new results for various fractional models involving the Fisher-KPP equation. Firstly, we prove that if the initial data lies between 0 and 1, then the global solution also belongs to the interval [0,1]. Secondly, we establish that the solution in the L^2 norm is bounded by the L^2 norm of the initial data. Lastly, we demonstrate that the model exhibits blow-up behavior on a finite time interval under certain conditions. Importantly, the results obtained in the non-commutative analysis cover many previously known results in the commutative case.