@inproceedings{Vieira,
author = {Vieira, Nelson},
title = {SOME RESULTS IN FRACTIONAL CLIFFORD ANALYSIS},
series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
organization = {Bauhaus-Universit{\"a}t Weimar},
issn = {1611-4086},
doi = {10.25643/bauhaus-universitaet.2825},
url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28256},
pages = {6},
abstract = {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.},
subject = {Angewandte Informatik},
language = {en}
}
@inproceedings{FerreiraVieira,
author = {Ferreira, Milton dos Santos and Vieira, Nelson},
title = {EIGENFUNCTIONS AND FUNDAMENTAL SOLUTIONS FOR THE FRACTIONAL LAPLACIAN IN 3 DIMENSIONS},
series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar},
editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom},
organization = {Bauhaus-Universit{\"a}t Weimar},
issn = {1611-4086},
doi = {10.25643/bauhaus-universitaet.2796},
url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27968},
pages = {6},
abstract = {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.},
subject = {Angewandte Informatik},
language = {en}
}