On the fuzzy initial value problem. (English) Zbl 0643.34005

Seikkala, Seppo

Fuzzy Sets Syst. 24, 319-330 (1987).

The paper deals with the initial value problem \(x'(t)=f(t,x(t)),\) \(x(0)=x_ 0\) with fuzzy initial value and with deterministic or fuzzy function f. The discussion refers to two different approaches (the extension principle and the use of extremal solutions, respectively), and includes also generalizations to fuzzy integral equations and fuzzy functional differential equations.

Reviewer: V.C.Boffi

MSC:

34A12

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

Keywords:

fuzzy initial value; fuzzy integral equations; fuzzy functional differential equations

References:

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