Fractional gradient and its application to the fractional advection equation

2013/05/19 by Mirko D’Ovidio, M. D'Ovidio, D'Ovidio, M. +3
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1305.4400

arxiv created 2013/05/19 · arxiv updated 2013/05/21

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 Lévy processes.

Citations

• Fractional Electromagnetic Equations Using Fractional Forms

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