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Mathematical Problems in Engineering
Volume 2016, Article ID 6380978, 13 pages
http://dx.doi.org/10.1155/2016/6380978
Research Article

Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order

Department of Mathematics, Faculty of Education for Girls, Kufa University, Najaf, Iraq

Received 17 July 2015; Accepted 13 October 2015

Academic Editor: Zhen-Lai Han

Copyright © 2016 Amal Khalaf Haydar and Ruaa Hameed Hassan. 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 main aim in this paper is to use all the possible arrangements of objects such that of them are equal to 1 and (the others) of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order ) for a fuzzy-valued function. Also, we find fuzzy Laplace transforms for Riemann-Liouville and Caputo fractional derivatives about the general fractional order under H-differentiability. Some fuzzy fractional initial value problems (FFIVPs) are solved using the above two generalizations.