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Abstract and Applied Analysis
Volume 2015, Article ID 659072, 14 pages
http://dx.doi.org/10.1155/2015/659072
Research Article

Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Received 28 May 2015; Accepted 8 September 2015

Academic Editor: Jianming Zhan

Copyright © 2015 Wichai Witayakiattilerd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The existence and uniqueness of a mild solution to nonlinear fuzzy differential equation constrained by initial value were proven. Initial value constraint was then replaced by delay function constraint and the existence of a solution to this type of problem was also proven. Furthermore, the existence of a solution to optimal control problem of the latter type of equation was proven.