The H functions, introduced by Fox in 1961, are special functions of a very general nature, which allow one to treat several phenomena including anomalous diffusion in a unified and elegant framework. In this paper we express the fundamental solutions of the Cauchy problem for the space-time fractional diffusion equation in terms of proper Fox H functions, based on their Mellin-Barnes integral representations. We pay attention to the particular cases of space-fractional, time-fractional and neutral-fractional diffusion.
Fox H functions in fractional diffusion / F. Mainardi; G. Pagnini; R.K. Saxena. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 178:(2005), pp. 321-331. [10.1016/j.cam.2004.08.006]
Fox H functions in fractional diffusion
MAINARDI, FRANCESCO;
2005
Abstract
The H functions, introduced by Fox in 1961, are special functions of a very general nature, which allow one to treat several phenomena including anomalous diffusion in a unified and elegant framework. In this paper we express the fundamental solutions of the Cauchy problem for the space-time fractional diffusion equation in terms of proper Fox H functions, based on their Mellin-Barnes integral representations. We pay attention to the particular cases of space-fractional, time-fractional and neutral-fractional diffusion.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
