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arXiv · 2502.11884

Trace operators for Riemann--Liouville fractional equations

Paola Loreti·Daniela Sforza
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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.

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Paola Loreti, Daniela Sforza. 2025-02-17. Trace operators for Riemann--Liouville fractional equations. https://arxiv.org/abs/2502.11884

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