We prove that the (nonlocal) Marchaud fractional derivative in R can be obtained from a parabolic extension problem with an extra (positive) variable as the operator that maps the heat conduction equation to the Neumann condition. Some properties of the fractional derivative are deduced from those of the local operator. In particular, we prove a Harnack inequality for Marchaud-stationary functions.
Bucur, C., Ferrari, F. (2016). An extension problem for the fractional derivative defined by Marchaud. FRACTIONAL CALCULUS & APPLIED ANALYSIS, 19(4), 867-887 [10.1515/fca-2016-0047].
An extension problem for the fractional derivative defined by Marchaud
Bucur C.
;
2016
Abstract
We prove that the (nonlocal) Marchaud fractional derivative in R can be obtained from a parabolic extension problem with an extra (positive) variable as the operator that maps the heat conduction equation to the Neumann condition. Some properties of the fractional derivative are deduced from those of the local operator. In particular, we prove a Harnack inequality for Marchaud-stationary functions.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
