Fractional gradient and its application to the fractional advection equation
Mathematical Physics
2013-05-21 v1 math.MP
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1305.4400,
title = {Fractional gradient and its application to the fractional advection equation},
author = {M. D'Ovidio and R. Garra},
journal= {arXiv preprint arXiv:1305.4400},
year = {2013}
}