Аннотация:
In this talk, a subordination principle for the solution operators to a family of the linear multi-dimensional space-time-fractional diffusion equations is addressed. These equations are obtained from the conventional diffusion equation by replacing the first order time-derivative by the Dzherbashyan-Caputo fractional derivative of order $\beta,\ 0 <\beta \leq 1$ and the Laplace operator by the fractional Laplacian $-(-\Delta)^{\frac\alpha 2}$ with $0<\alpha \leq 2$. First, a representation of the fundamental solutions to these equations is obtained in form of a Mellin-Barnes type integral. This representation is then employed for derivation of a subordination formula that connects the solution operator to the space-time-fractional diffusion equation with the orders $\alpha$ and $\beta$ of the fractional derivatives with the fundamental solution to the conventional diffusion equation.
Язык доклада: английский
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