**Preprint No.**
A-98-07

#
R. Gorenflo, F. Mainardi

## Signalling Problem and Dirichlet-Neumann map for time-fractional diffusion-wave equations

**Abstract:** The time-fractional, spatially one-dimensional, diffusion-wave
equation is considered. For the Dirichlet and the Neumann condition
prescribed on the boundary of the spatial positive half-line and
zero-initial condition at the origin of time the solutions are derived via
the method of Laplace transforms, and it is shown that the
Dirichlet-Neumann map is given by a time-fractional differential
operator whose order is (in analogy to the cases of the classical diffusion
and wave equation) half the order of the time-fractional derivative.
**Mathematics Subject Classification (MSC91):** 26A33 Fractional derivatives and integrals
, 45K05 Integro-partial differential equations

**Language:** ENG
**Available:** Pr-A-98-07.ps

**Contact**: Gorenflo, R.; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (gorenflo@math.fu-berlin.de)

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