Affiliation:
1. School of Technology and Management Polytechnic Institute of Leiria P-2411-901 , Leiria , Portugal
2. Center for Research and Development in Mathematics and Applications (CIDMA) , Department of Mathematics University of Aveiro, Campus Universitário de Santiago 3810-193 Aveiro , Portugal
Abstract
Abstract
In this paper we study the fundamental solution (FS) of the multidimensional time-fractional telegraph equation where the time-fractional derivatives of orders α ∈]0,1] and β ∈]1,2] are in the Caputo sense. Using the Fourier transform we obtain an integral representation of the FS in the Fourier domain expressed in terms of a multivariate Mittag-Leffler function. The Fourier inversion leads to a double Mellin-Barnes type integral representation and consequently to a H-function of two variables. An explicit series representation of the FS, depending on the parity of the dimension, is also obtained. As an application, we study a telegraph process with Brownian time. Finally, we present some moments of integer order of the FS, and some plots of the FS for some particular values of the dimension and of the fractional parameters α and β.
Subject
Applied Mathematics,Analysis
Reference19 articles.
1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 10th printing. National Bureau of Standards, Wiley-Interscience Publication, John Wiley & Sons, New York etc. (1972).
2. R.G. Buschman, H-functions of two variables, III. Pure Appl. Math. Sci. 9 (1978), 13–18.
3. R.G. Buschman, H-functions of two variables, I. Indian J. Math. 20 (1978), 132–153.
4. R.F. Camargo, A.O. Chiacchio, E.C. de Oliveira, Differentiation to fractional orders and the fractional telegraph equation. J. Math. Phys. 49, No 3 (2008), Article ID 033505, 12p; 10.1063/1.2890375.
5. R.C. Cascaval, E.C. Eckstein, L.C. Frota, J.A. Goldstein, Fractional telegraph equations. J. Math. Anal. Appl. 276, No 1 (2002), 145–159; 10.1016/S0022-247X(02)00394-3.
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