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 Ψn (coinciding with the one governed by the standard, non-fractional, equation) with a time argument Ta which is itself random. The distribution of Ta is presented together with some features of the solution (such as analytic expressions for its moments).
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