A new approach to linear interval differential equations as a first step toward solving fuzzy differential - da Costa, Tiago M.; Chalco-Cano, Yurilev; Lodwick, Weldon A.; Silva, Geraldo N. [UNESP] (Elsevier, 2018)
This study uses a concept of interval differentiability, which was recently introduced, to formulate interval initial value problems involving linear interval differential equations. Differently from the approaches that use the gH-differentiability, this study does not make use of a criterion of choice for switching points in order to obtain solutions for such problems. The method herein presented provides solutions in a simple, straightforward, and computationally tractable way. Moreover, these solutions are intuitive because they coincide with the solutions given by a differential inclusion method. The efficiency and practicality of our approach are illustrated through some examples that have appeared in other articles.
Keywords: Interval differentiability; Interval initial value problems; Interval linear differential equations; Interval-valued functions