582 citations · 798 across the 15 of their papers we have counts for
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math.AP2015★ 15 cited
An extension problem for the fractional derivative defined by Marchaud
Claudia Bucur, Fausto Ferrari
We prove that the (nonlocal) Marchaud fractional derivative in can be obtained from a parabolic extension problem with an extra (positive) variable, as the operator th…
math.AP2015★ 582 cited
Nonlocal diffusion and applications
Claudia Bucur, Enrico Valdinoci
We consider the fractional Laplace framework and provide models and theorems related to nonlocal diffusion phenomena. Some applications are presented, including: a simple probabili…
math.AP2015★ 125 cited
Some observations on the Green function for the ball in the fractional Laplace framework
Claudia Bucur
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, o…