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Pseudo-Processes Governed by Higher-Order Fractional Differential Equations

   
@article{EJP496,
	author = {Luisa Beghin},
	title = {Pseudo-Processes Governed by Higher-Order Fractional Differential Equations},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {Higher-order heat-type equations; Fractional derivatives; Wright functions; Stable laws.},
	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.},
	pages = {no. 16, 467-485},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-496},    
        url = {http://ejp.ejpecp.org/article/view/496}}