The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then, by using the Mellin transform, a general representation of the Green function in terms of Mellin-Barnes integrals in the complex plane is derived. This allows us to obtain a suitable computational form of the Green function in the space-time domain and to analyse its probability interpretation.

Applications of integral transforms in fractional diffusion processes

MAINARDI, FRANCESCO
2004

Abstract

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then, by using the Mellin transform, a general representation of the Green function in terms of Mellin-Barnes integrals in the complex plane is derived. This allows us to obtain a suitable computational form of the Green function in the space-time domain and to analyse its probability interpretation.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/17732
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