Hidden trace regularity for Riemann–Liouville fractional equations

Abstract

We begin with a brief overview of the most commonly used fractional derivatives, namely, the Caputo and Riemann–Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann–Liouville derivative, addressing key questions such as well-posedness, regularity, and a trace result in appropriate interpolation spaces. Additionally, we explore the duality relationship with the Caputo fractional time derivative. The analysis is based on expanding the solution in terms of Mittag-Leffler functions.