582 citations · 798 across the 15 of their papers we have counts for
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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…
Local density of Caputo-stationary functions in the space of smooth functions
Claudia Bucur
We consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any function can…
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…
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…