Definite Solution Problems Of Fuzzy Differential Equation

In this article we introduce the fuzzy numbers with bounded support and strictly fuzzy convexity and give the couple parametric representation of fuzzy numbers. By the parametric representation, fuzzy number means a bounded continuous curve in the two-dimensional metric space R 2, or a point of some Banach space where the addition is the same one due to the extension principle but the difference and scalar products are not the same as those of the extension principle. We show that the fuzzy number space is a closed convex cone in the Banach space.In addition, by the theory of Banach space, we define the differential and integral of fuzzy-number-valued functions and give the properties, further, we show the relation between H-differentiation and differentiation. On this basis, we treat initial value problems of first-order fuzzy differential equations and initial value problem of higher order fuzzy differential equation, and show that they can be transformed into a kind of initial value problem of first-order fuzzy differential equation, we give existence and uniqueness theorem and sufficient conditions of solutions.Finally, we treat two-point boundary value problem of fuzzy differential equation under the H-differentiability, in [39] the author asserts that two-point boundary value problem of fuzzy differential equation is equivalent to an integral equation, we prove by a counterexample that this assertion does not hold. Moreover, it is proved that a large class of two-point boundary value problems of fuzzy differential equation has no solutions at all under the H-differentiability.