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.
Hidden trace regularity for Riemann–Liouville fractional equations / Loreti, Paola; Sforza, Daniela. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 36:1(2025), pp. 139-165. [10.4171/rlm/1067]
Hidden trace regularity for Riemann–Liouville fractional equations
Loreti, Paola;Sforza, Daniela
2025
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.


