A discretization for the nonlinear parabolic evolution equation of fractional order in space
This work addresses a domain-specific problem in numerical analysis for fractional PDEs, but it appears incremental as it focuses on a new discretization method without clear broad impact.
The authors tackled the numerical discretization of a nonlinear parabolic equation with fractional order in space, using a functional analytic definition for the fractional derivative instead of traditional ones like Riemann-Liouville, and reported numerical experiments with conjectures.
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.