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On the Fractional Wave Equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Francesco Iafrate & Enzo Orsingher, 2020. "On the Fractional Wave Equation," Mathematics, MDPI, vol. 8(6), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:874-:d:365306
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