Autor(es): Ferreira, M. ; Kraußhar, R. S. ; Rodrigues, M. M. ; Vieira, N.
Data: 2019
Identificador Persistente: http://hdl.handle.net/10400.8/5525
Origem: IC-online
Assunto(s): Fractional Clifford analysis; Fractional derivatives; Stokes's formula; Borel-Pompeiu formula; Cauchy's integral formula; Hodge-type decomposition
In this paper, we develop a fractional integro-differential operator calculus for Clifford-algebra valued functions. To do that we introduce fractional analogs of the Teodorescu and Cauchy-Bitsadze operators and we investigate some of their mapping properties. As a main result, we prove a fractional Borel-Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge-type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann-Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order.
