On the Fractional Wave Equation
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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.
multivariate stable processes, contour integrals, General Mathematics, Computer Science (miscellaneous), Hankel contours, QA1-939, fractional laplacian, Contour integrals; Fractional laplacian; Hankel contours; Multivariate stable processes, Engineering (miscellaneous), Mathematics
multivariate stable processes, contour integrals, General Mathematics, Computer Science (miscellaneous), Hankel contours, QA1-939, fractional laplacian, Contour integrals; Fractional laplacian; Hankel contours; Multivariate stable processes, Engineering (miscellaneous), Mathematics
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