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.
Articolo in rivista - Articolo scientifico
degenerate parabolic PDEs; extension problems; fractional derivative; Harnack inequality; Marchaud derivative
English
2016
19
4
867
887
none
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].
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.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/277782
Citazioni
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 11
Social impact