Pseudo-processes governed by higher-order fractional differential equations

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 $T_{\alpha}$ which is itself random. The distribution of $T_{\alpha}$ is presented together with some features of the solution (such as analytic expressions for its moments).