TY - CHAP
A1 - Vieira, Nelson
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - SOME RESULTS IN FRACTIONAL CLIFFORD ANALYSIS
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - What is nowadays called (classic) Clifford analysis consists in the establishment of a function theory for functions belonging to the kernel of the Dirac operator. While such functions can very well describe problems of a particle with internal SU(2)-symmetries, higher order symmetries are beyond this theory. Although many modifications (such as Yang-Mills theory) were suggested over the years they could not address the principal problem, the need of a n-fold factorization of the d’Alembert operator. In this paper we present the basic tools of a fractional function theory in higher dimensions, for the transport operator (alpha = 1/2 ), by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville derivatives. A Fischer decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Building Information Modeling
KW - Computerunterstütztes Verfahren
KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28256
SN - 1611-4086
ER -
TY - CHAP
A1 - Ferreira, Milton dos Santos
A1 - Vieira, Nelson
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - EIGENFUNCTIONS AND FUNDAMENTAL SOLUTIONS FOR THE FRACTIONAL LAPLACIAN IN 3 DIMENSIONS
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - Recently there has been a surge of interest in PDEs involving fractional derivatives in different fields of engineering. In this extended abstract we present some of the results developedin [3]. We compute the fundamental solution for the three-parameter fractional Laplace operator Δ by transforming the eigenfunction equation into an integral equation and applying the method of separation of variables. The obtained solutions are expressed in terms of Mittag-Leffer functions. For more details we refer the interested reader to [3] where it is also presented an operational approach based on the two Laplace transform.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Building Information Modeling
KW - Computerunterstütztes Verfahren
KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27968
SN - 1611-4086
ER -