Trace regularity for biharmonic evolution equations with Caputo derivatives

TL;DR

This paper investigates the regularity properties of solutions to a time fractional Petrovsky system involving Caputo derivatives of order between 1 and 2, revealing hidden regularity for weak solutions.

Contribution

It establishes a new hidden regularity result for solutions of the fractional Petrovsky system with Caputo derivatives, expanding understanding of fractional PDEs.

Findings

Hidden regularity for weak solutions proven

Applicable to Caputo derivatives of order between 1 and 2

Advances the theory of fractional evolution equations

Abstract

Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky system where the Caputo fractional derivative is of order $\alpha\in(1,2)$. We achieve such result for a suitable class of weak solutions.