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Journal of Function Spaces
Volume 2016, Article ID 6086409, 9 pages
http://dx.doi.org/10.1155/2016/6086409
Research Article

Fractional Calculus of Analytic Functions Concerned with Möbius Transformations

1Department of Mathematics-Informatics, Faculty of Sciences, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
2Department of Mathematics, Faculty of Education, Yamato University, Katayama 2-5-1, Suita, Osaka 564-0082, Japan

Received 17 October 2015; Accepted 3 March 2016

Academic Editor: Simone Secchi

Copyright © 2016 Nicoleta Breaz 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

Let be the class of functions in the open unit disk with and . Also, let be a Möbius transformation in for some . Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals) of . Also, some interesting examples for fractional calculus are given.