Interval Cauchy problem with a second type Hukuhara derivative

In this paper we consider interval differential equations. Such the equations can be appropriate in modeling of dynamical systems under presence of uncertainty of parameters. We study an interval initial value problem with a second type Hukuhara derivative. By an example of real-world application we indicate the advantages of the usage of such a kind of interval-valued derivative. A continuous dependence of the solution on initial value and right-hand side of the equation is shown. The existence of approximate local solutions is proven, and then it is used in the derivation of existence of at least one local solution to interval Cauchy problem with second type Hukuhara derivative. The compactness of solutions set is also stated. Finally, the explicit formulae for local solutions to linear interval differential equations are provided.