Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense

• Autor(a) principal: Teodoro, A. Di
• Data de Publicação: 2020
• Outros Autores: Ferreira, M., Vieira, N.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/27160
• topic: Fractional Clifford Analysis; Fractional derivatives; Fundamental solution; Poisson's equation; Laplace transform

In this paper, we study the fundamental solution for natural powers of the $n$-parameter fractional Laplace and Dirac operators defined via Riemann-Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace $\Delta_{a^+}^\alpha$ and Dirac $D_{a^+}^\alpha$ operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag-Leffler function.