On the Fractional Wave Equation

Francesco Iafrate and Enzo Orsingher
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Francesco Iafrate: Dipartimento di Scienze Statistiche, Sapienza, University of Rome, 00185 Rome, Italy
Enzo Orsingher: Dipartimento di Scienze Statistiche, Sapienza, University of Rome, 00185 Rome, Italy

Mathematics, 2020, vol. 8, issue 6, 1-14

Abstract: In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d −dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

Keywords: Hankel contours; multivariate stable processes; contour integrals; fractional laplacian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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