Fundamental solution of the time-fractional telegraph Dirac operator

• Autor(a) principal: Ferreira, Milton dos Santos
• Data de Publicação: 2017
• Outros Autores: Rodrigues, Maria Manuela Fernandes, Vieira, Nelson Felipe Loureiro
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/21071
• topic: Time-fractional telegraph and telegraph Dirac operators; Fundamental solution; Caputo fractional derivative; Multivariate Mittag-Leffler functions; H-function of two variables

In this work we obtain the fundamental solution (FS) of the multidimensional time-fractional telegraph Dirac operator where the two time-fractional derivatives of orders $\alpha \in ]0,1]$ and $\beta \in ]1,2]$ are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters $\alpha$ and $\beta$. Finally, using the FS we study some Poisson and Cauchy problems.