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.
F. Mainardi (2004). Applications of integral transforms in fractional diffusion processes. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 15, 477-484 [10.1080/10652460412331270652].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
