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Limit Theorems for the Dynamical Foundation of the Fractional Brownian Motion and Related Models of Anomalous Diffusion with Random Diffusion Coefficient and Time-Dependent Random Hurst parameter
Christian Bender, Yana A. Butko, Mirko D'Ovidio +1
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most r…
Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs
Stefano Bonaccorsi, Fausto Colantoni, Mirko D'Ovidio +1
We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random time…
The tempered space-fractional Cattaneo equation
Luisa Beghin, Roberto Garra, Francesco Mainardi +1
We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we expla…
Mellin transform and subordination laws in fractional diffusion processes
Francesco Mainardi, Gianni Pagnini, Rudolf Gorenflo
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted…