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Journal of Function Spaces and Applications
Volume 2013, Article ID 543839, 7 pages
Research Article

The -Fractional Analogue for Gronwall-Type Inequality

1Department of Mathematics and Computer Science, Çankaya University, Ögretmenler Caddesi 14, Balgat, 06530 Ankara, Turkey
2Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

Received 8 May 2013; Accepted 7 July 2013

Academic Editor: Dashan Fan

Copyright © 2013 Thabet Abdeljawad and Jehad O. Alzabut. 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.


We utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used. An example is given to illustrate the validity of the derived inequality.