Available online at www.ispacs.com/jfsva Volume 2012, Year 2012 Article ID jfsva-00136, 19 pages doi:10.5899/2012/jfsva-00136 Research Article Solution of the Fuzzy Boundary Value Differential Equations Under Generalized Differentiability By Shooting Method L. Jamshidi 1 , L. Avazpour 2* (1)Department of Mathematics, Science and Research Branch, Islamic Azad University, Hamedan, Iran. (2)Department of Mathematics, Yasouj Branch, Islamic Azad University, Yasouj, Iran. Copyright 2012 c ⃝L. Jamshidi and L. Avazpour. 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 In this paper, we apply the shooting method for solving the Fuzzy Boundary Value Differ- ential Equations (FBVDEs) of the second order under generalized differentiability. By this method an FBVDE of the second order will be replaced with two fuzzy initial value differ- ential equations and the answers of each of them are obtained by the Adomian method. Finally via linear combination of their solutions, the fuzzy solution will be obtained. Keywords : Shooting method; Fuzzy Boundary Value Differential Equations ; Generalized differen- tiability ; Adomian method. 1 Introduction The theory of fuzzy differential equations (FDEs) has attracted much attention in recent times because this theory represents a natural way to model dynamical systems under uncertainty. The concept of the fuzzy derivative was first introduced by Chang and Zadeh [12]; it was followed up by Dubois and Prade [16], who used the extension principle in their approach. The study of fuzzy differential equations has been initiated as an independent subject in conjunction with fuzzy valued analysis [17] and [22] and set-valued differential equations [21]. Initially, the derivative for fuzzy valued mappings was developed by Puri and Ralescu [24], that generalized and extended the concept of Hukuhara differentiability (H-derivative) for set-valued mappings to the class of fuzzy mappings. Subsequently, using the H-derivative, Kaleva [19] started to develop a theory for FDE. In the last few * Corresponding author. Email address: avazpour.l@gmail.com, Tel:+989173414337. 1