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Advances in Mathematical Physics
Volume 2015, Article ID 719173, 8 pages
http://dx.doi.org/10.1155/2015/719173
Research Article

Spatial Rotation of the Fractional Derivative in Two-Dimensional Space

Department of Physics, United Arab Emirates University, Al Ain, UAE

Received 27 May 2015; Accepted 12 July 2015

Academic Editor: Soheil Salahshour

Copyright © 2015 Ehab Malkawi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The transformations of the partial fractional derivatives under spatial rotation in are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed through fractional derivatives, with respect to different coordinate systems (observers). It is the hope that such understanding could shed light on the physical interpretation of fractional derivatives. Also it is necessary to be able to construct interaction terms that are invariant with respect to equivalent observers.