5 documents found, page 1 of 1
Hypercomplex operator calculus for the fractional Helmholtz equation
Vieira, N.; Ferreira, M.; Rodrigues, M. M.; Kraußhar, R. S.In this paper, we develop a hypercomplex operator calculus to treat fully analytically boundary value problems for the homogeneous and inhomogeneous fractional Helmholtz equations where fractional derivatives in the sense of Caputo and Riemann-Liouville are applied. Our method extends the recently proposed Fractional Reduced Differential Transform Method (FRDTM) by using fractional derivatives in all directions...
The Teodorescu and the Π-operator in octonionic analysis and some applications
Kraußhar, R. S.; Ferreira, M.; Vieira, N.; Rodrigues, M. M.In the development of function theory in octonions, the non-associativity property produces an additional associator term when applying the Stokes formula. To take the non-associativity into account, particular intrinsic weight factors are implemented in the definition of octonion-valued inner products to ensure the existence of a reproducing Bergman kernel. This Bergman projection plays a pivotal role in the $...
Variational Principles in Quaternionic Analysis with Applications to the Statio...
Cerejeiras, Paula; Kahler, Uwe; Kraußhar, R. S.In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing geometry independent explicit global existence and uniqueness criteria as well as new computational methods with special focus to the stationary incompressible viscous magneto...
A higher dimensional fractional Borel‐Pompeiu formula and a related hypercomple...
Ferreira, M.; Kraußhar, R. S.; Rodrigues, M. M.; Vieira, N.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 d...
Application of the hypercomplex fractional integro-differential operators to th...
Ferreira, M.; Kraußhar, R. S.; Rodrigues, M. M.; Vieira, N.We present a generalization of several results of the classical continuous Clifford function theory to the context of fractional Clifford analysis. The aim of this paper is to show how the fractional integro-differential hypercomplex operator calculus can be applied to a concrete fractional Stokes problem in arbitrary dimensions which has been attracting recent interest (cf. \cite{CNP,LAX}).