Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those equations, the explicit laws of certain stable processes turn out to be fundamental. This paper directs one's efforts towards the explicit representation of solutions to fractional and anomalous diffusions related to Sturm-Liouville problems of fractional order associated to fractional power function spaces. Furthermore, we study a new version of Bochner's subordination rule and we establish some connections between subordination and space-fractional operators. (C) 2012 Elsevier B.V. All rights reserved.

From Sturm-Liouville problems to fractional and anomalous diffusions / D'Ovidio, Mirko. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 122:10(2012), pp. 3513-3544. [10.1016/j.spa.2012.06.002]

From Sturm-Liouville problems to fractional and anomalous diffusions

D'OVIDIO, MIRKO
2012

Abstract

Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those equations, the explicit laws of certain stable processes turn out to be fundamental. This paper directs one's efforts towards the explicit representation of solutions to fractional and anomalous diffusions related to Sturm-Liouville problems of fractional order associated to fractional power function spaces. Furthermore, we study a new version of Bochner's subordination rule and we establish some connections between subordination and space-fractional operators. (C) 2012 Elsevier B.V. All rights reserved.
2012
sturm-liouville problem; fox functions; sturm-liouville problem; stable subordinator; anomalous diffusion; mellin convolution
01 Pubblicazione su rivista::01a Articolo in rivista
From Sturm-Liouville problems to fractional and anomalous diffusions / D'Ovidio, Mirko. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 122:10(2012), pp. 3513-3544. [10.1016/j.spa.2012.06.002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/480488
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