On fuzzy boundary value problems

Approximate solution of second-order fuzzy boundary value problem

“…The concept of fuzzy numbers was introduced by Zadeh [11,30]. By using H-derivative, several articles [26,12,13] have demonstrated the solution to the fuzzy differential equations. However, Bede and Gal [7] introduced a generalized definition for fuzzy derivative and a fuzzy-number-valued function.…”

The Cauchy problems for discontinuous fuzzy systems under generalized differentiability

“…Because the metric space (E n , D) has a linear structure, it can be imbedded isomorphically as a cone in a Banach space. It is worth mentioning that Chen et al [4][5][6] studied the initial value problems of fuzzy differential equations by using the parametric representation of fuzzy numbers and the new framework of calculus for fuzzy number valued functions established in [7]. One can see that their method was more convenient than the original method to calculate derivatives, integrals and compute numerical solutions, etc.…”

Improved predictor–corrector method for solving fuzzy initial value problems

“…The concept of a fuzzy derivative was first introduced by Chang and Zadeh [10], and followed by Dubois and Prade [14], who defined and used the extension principle. The fuzzy differential equation and the fuzzy initial value problem were defined by Nieto and Rodriguez-Lopez [25], Seikkala [32], and many other researchers [3,7,9,[11][12][13]16,18,19,21,23,24,[26][27][28][29][30][31]34,35]. Numerical methods for solving FDEs are introduced in [1,2,5,6,17,22].…”