Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:447

Article

Ferreira, M.^1,2  Vieira, N.² 

[1] Polytech Inst Leiria, Sch Technol & Management, P-2411901 Leiria, Portugal

[2] Univ Aveiro, Dept Math, CIDMA Ctr Res & Dev Math & Applicat, Campus Univ Santiago, P-3810193 Aveiro, Portugal

关键词: Time fractional diffusion-wave operator;    Time fractional parabolic Dirac operator;    Fundamental solutions;    Caputo fractional derivative;    Fractional moments;   

DOI  :  10.1016/j.jmaa.2016.08.052

来源: Elsevier

【 摘 要 】

In this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order beta is an element of]0, 2]. Applying operational techniques via Fourier and Mellin transforms we obtain an integral representation of the fundamental solution (FS) of the time fractional diffusion-wave operator. Series representations of the FS are explicitly obtained for any dimension. From these we derive the FS for the time fractional parabolic Dirac operator in the form of integral and series representation. Fractional moments of arbitrary order gamma > 0 are also computed. To illustrate our results we present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameter. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free