A discretization for the nonlinear parabolic evolution equation of fractional order in space

TL;DR

This paper introduces a novel numerical discretization method for a nonlinear fractional-order parabolic equation, utilizing a functional analytic approach to define the fractional derivative.

Contribution

It proposes a new discretization technique based on a functional analytic framework, differing from traditional fractional derivative definitions.

Findings

Numerical experiments demonstrate the effectiveness of the proposed discretization.

The approach offers a new perspective on defining fractional derivatives in PDEs.

Abstract

We consider a nonlinear parabolic equation of fractional order in space and propose its numerical discretization. The fractional derivative is defined through a functional analytic setting, rather than the traditional definition of fractional derivatives such as the Riemann-Liouville derivative. Numerical experiments are reported and some conjectures are presented.