First order linear fuzzy differential equations under generalized differentiability

First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.