Pseudo-Processes Governed by Higher-Order Fractional Differential Equations

Luisa Beghin (University of Rome)

Abstract


We study here a heat-type differential equation of order $n$ greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess $\Psi _{n}$ (coinciding with the one governed by the standard, non-fractional, equation) with a time argument $\mathcal{T}_{\alpha }$ which is itself random. The distribution of $\mathcal{T}_{\alpha }$ is presented together with some features of the solution (such as analytic expressions for its moments.

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Pages: 467-485

Publication Date: March 31, 2008

DOI: 10.1214/EJP.v13-496

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