On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation

Document Type : Research Paper

Authors

1 Young Researchers and Elites Club, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, ‎Iran.

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, ‎Iran.

Abstract

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara differentiability, the analytical solution of an exact second order fuzzy initial value problem is derived in two senses of differentiability. Also, several properties for generalized Hukuhara differentiability are obtained on the topics, such as, the univariate fuzzy chain rules, fuzzy integration by parts, among others. At the end, some illustrative examples are presented and these examples show the behavior of the ‎solutions.‎

Keywords

International Journal of Industrial Mathematics
Volume 9, Issue 4
September 2017
Pages 279-288

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