Solving the BVP to a class of second-order linear fuzzy differential equations under granular differentiability concept1

Abstract

Based on the granular derivative and the horizontal membership function of fuzzy-number-valued-function, the existence and uniqueness of solutions of two-point boundary value problem (BVP) for a class of second-order linear fuzzy ordinary differential equations are given, including the homogeneous BVP, the semi-homogeneous BVP and the non-homogeneous BVP. However, this is somewhat different from ordinary differential equations. In fact, we can think of it simply as the transformation from a number to a set, or we can think of it macroscopically as the transformation from a point to a plane. At the same time, appropriate examples are given to illustrate this conclusion.