On the existence of approximate solutions to fuzzy delay differential equations under the metric derivative

In this paper, we use a metric derivative which is based on the Hausdorff distance between fuzzy numbers. Using this concept of differentiability, we study fuzzy delay differential equations and also prove a result which guarantees the existence of the approximate solutions. The proof of this result is constructive and provides a method to obtain approximate solutions based on fuzzy arithmetic. In order to illustrate the applicability of the presented results, we provide an example with Hutchinson equation and other with a two-dimensional system.