# Spectral approximation of fractional PDEs in image processing and phase field modeling

## TL;DR

This paper develops a spectral approximation method for fractional PDEs, demonstrating its effectiveness in image processing and phase field modeling through theoretical analysis and numerical experiments.

## Contribution

It introduces a spectral numerical scheme for fractional PDEs and analyzes its efficiency, specifically applied to image processing and phase field models.

## Key findings

- Spectral method effectively approximates fractional PDEs.
- Numerical experiments confirm the method's efficiency.
- Applications include image processing and phase field modeling.

## Abstract

Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.