publication . Preprint . 2013

Fractional gradient and its application to the fractional advection equation

D'Ovidio, M.; Garra, R.;
Open Access English
  • Published: 19 May 2013
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\'evy processes.
free text keywords: Mathematical Physics, Mathematics - Probability
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X(x) = 2

4(f (x + y) > 0 a shape parameter. We observe that

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