Repositório Institucional da Universidade de Aveiro > CIDMA - Centro de Investigação e Desenvolvimento em Matemática e Aplicações > CIDMA - Artigos > Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
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 title: Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators authors: Ferreira, Milton dos SantosVieira, Nelson Felipe Loureiro keywords: Fractional Laplace operatorRiemann-Liouville fractional derivativesEigenfunctionsMittag-Leffler functionTime fractional diffusion-wave operatorTime fractional parabolic Dirac operatorFundamental solutionsCaputo fractional derivativeFractional moments issue date: 1-Mar-2017 publisher: Elsevier abstract: In this paper we study the multidimensional time fractional diffusion-wave equation where the time fractional derivative is in the Caputo sense with order $\beta \in ]0,2].$ 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. URI: http://hdl.handle.net/10773/16282 ISSN: 0022-247X publisher version/DOI: http://dx.doi.org/10.1016/j.jmaa.2016.08.052 source: Journal of Mathematical Analysis and Applications appears in collections CIDMA - Artigos

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