Author(s):
Ferreira, M. ; Luchko, Yu. ; Rodrigues, M. M. ; Vieira, N.
Date: 2020
Persistent ID: http://hdl.handle.net/10400.8/5523
Origin: IC-online
Project/scholarship:
info:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND/01131/2018/CP1559/CT0014/PT;
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB/04106/2020/PT;
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP/04106/2020/PT;
Subject(s): Time-fractional diffusion-wave operator Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series.; Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series
Description
In this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time-fractional diffusion-wave operator with the time-fractional derivative of order $\beta \in ]1,2[$ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier-Bessel transform and as double contour integrals of the Mellin-Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any $\beta \in ]1,2[$ and as Kamp\'{e} de F\'{e}riet and Lauricella series in two variables for the rational values of $\beta$. The limit cases $\beta=1$ (diffusion operator) and $\beta=2$ (wave operator) as well as an intermediate case $\beta=\frac{3}{2}$ are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order $\beta$ and the spatial dimension $n$.
