Boundary Value Problems
Volume 2009 (2009), Article ID 395714, 13 pages
doi:10.1155/2009/395714
Research Article

New Results on Multiple Solutions for Nth-Order Fuzzy Differential Equations under Generalized Differentiability

A. Khastan,1,2 F. Bahrami,1,2 and K. Ivaz1,2

1Department of Applied Mathematics, University of Tabriz, Tabriz 51666 16471, Iran
2Research Center for Industrial Mathematics, University of Tabriz, Tabriz 51666 16471, Iran

Received 30 April 2009; Accepted 1 July 2009

Academic Editor: Juan José Nieto

Copyright © 2009 A. Khastan 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 firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We present an example of a linear second-order fuzzy differential equation with initial conditions having four different solutions.