Stochastic solution of a nonlinear fractional differential equation

TL;DR

This paper develops a stochastic method to solve a nonlinear fractional differential equation, extending classical processes with Levy-based spectral integrals to handle fractional derivatives.

Contribution

It introduces a novel stochastic solution framework for a fractional KPP equation using generalized branching and propagation processes based on Levy processes.

Findings

Successfully constructs a stochastic solution for the fractional KPP equation.

Extends classical branching processes to fractional derivatives using Levy spectral integrals.

Provides a new probabilistic approach for nonlinear fractional differential equations.

Abstract

A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes