JID:FSS AID:6598 /FLA [m3SC+; v 1.194; Prn:30/07/2014; 16:11] P.1(1-15) Available online at www.sciencedirect.com ScienceDirect Fuzzy Sets and Systems ••• (••••) •••–••• www.elsevier.com/locate/fss Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles ✩ Elder J. Villamizar-Roa a,1 , Vladimir Angulo-Castillo a , Yurilev Chalco-Cano b,∗ a Universidad Industrial de Santander, Escuela de Matemáticas, A.A.678, Bucaramanga, Colombia b Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile Received 28 October 2013; received in revised form 29 April 2014; accepted 20 July 2014 Abstract We study the existence and uniqueness of solution for fuzzy initial value problems in the setting of a generalized Hukuhara derivative and by using some recent results of fixed point of weakly contractive mappings on partially ordered sets.  2014 Elsevier B.V. All rights reserved. Keywords: Contractive mappings; Fuzzy differentiability; Fuzzy differential equations 1. Introduction Fuzzy differential equations (FDE) are a suitable tool to model dynamic systems in which uncertainties or vague- ness pervade. This theory has been developed in several theoretical directions, and a wide number of applications in many different real problems have been considered (see for instance [3–5,9,18,22,28,34,37–39]). Several settings for studying FDE have been considered. The first and the most popular approach is using the Hukuhara differentia- bility (H-differentiability) for fuzzy value functions (see for instance [21,28,32,34]). However, this approach has the drawback that the solution of a fuzzy differential equation needs to have increasing length of its support, so, is in this case, the qualitative theory very poor compared to ODEs [3,5,8,11,14,15]. In order to overcome this weakness some alternatives have been proposed; in fact, in [4] was introduced the concept of strongly generalized differentia- bility (GH-differentiability) which allows us to obtain new solutions of fuzzy differential equations as it was shown in [5,11,23,24]. This concept of differentiability is based on four forms (types) of lateral derivatives. The differen- tiability in the first form (i) coincides with the H-differentiability and then the GH-differentiability is more general ✩ This work has been partially supported by Conicyt-Chile through Projects Fondecyt 1120665 and VIE-UIS, proyecto:C-2013-01. * Corresponding author. Tel.: +56 58 2230334. E-mail addresses: jvillami@uis.edu.co (E.J. Villamizar-Roa), ychalco@uta.cl (Y. Chalco-Cano). 1 The first author has been supported by VIE-UIS, proyecto:C-2013-01. http://dx.doi.org/10.1016/j.fss.2014.07.015 0165-0114/ 2014 Elsevier B.V. All rights reserved.