Higher Order Initial Value Problem with Interactive Fuzzy Conditions

Abstract

In this manuscript we deal with non-homogeneous n-th order linear differential equations that have fuzzy initial conditions. We assume that the initial conditions are given by fuzzy numbers that satisfying a special type of relationship namely interactivity. In particular, we assume that the initial conditions are completely correlated fuzzy numbers. Based on this notion, we obtain solutions for linear fuzzy initial value problems by means of the extension principle. Finally, we show that endpoints of each α-level of the proposed solution can be determined by solving two associated classical initial value problems.