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arXiv · 1305.4400

Fractional gradient and its application to the fractional advection equation

M. D'Ovidio·R. Garra
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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.

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M. D'Ovidio, R. Garra. 2013-05-19. Fractional gradient and its application to the fractional advection equation. https://arxiv.org/abs/1305.4400

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