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Abstract and Applied Analysis
Volume 2014, Article ID 392598, 8 pages
http://dx.doi.org/10.1155/2014/392598
Research Article

On Fractional Derivatives and Primitives of Periodic Functions

1Departamento de Matemática Aplicada II, E.E. Telecomunicación, Universidade de Vigo, 36310 Vigo, Spain
2Facultad de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
3Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 23 May 2014; Revised 8 July 2014; Accepted 8 July 2014; Published 14 August 2014

Academic Editor: Hari M. Srivastava

Copyright © 2014 I. Area et al. 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

We prove that the fractional derivative or the fractional primitive of a -periodic function cannot be a -periodic function, for any period , with the exception of the zero function.