Relationship between Bede–Gal differentiable set-valued functions and their associated support functions

In this study, we adapt the concept of the Bede–Gal derivative, which was initially suggested for fuzzy number-valued functions, to set-valued functions. We use an example to demonstrate that this concept overcomes some of the shortcomings of the Hukuhara derivative.We prove some properties of Bede–Gal differentiable set-valued functions. We also study the relationship between a Bede–Gal differentiable set-valued function and its value's support function, which we call the associated support function. We provide examples of set-valued functions that are not Bede–Gal differentiable whereas their associated support functions are differentiable. We also present some applications of the Bede–Gal derivative to solving set-valued differential equations.