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


Contact: Gorenflo, R.; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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