Eigenfunctions of the time‐fractional diffusion‐wave operator

• Autor(a) principal: Ferreira, Milton
• Data de Publicação: 2021
• Outros Autores: Luchko, Yury, Rodrigues, M. Manuela, Vieira, Nelson
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/29993
• topic: Time-fractional diffusion-wave operator; Eigenfunctions; Caputo fractional derivatives; Generalized hypergeometric series

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 β ∈]1, 2[ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier–Bessel transform and as a double contour integrals of the Mellin–Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any β ∈]1, 2[ and as Kampé de Fériet and Lauricella series in two variables for the rational values of β. The limit cases =1 (diffusion operator) and =2 (wave operator) as well as an intermediate case =32 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 β and the spatial dimension n.