The existence and uniqueness theorems of fuzzy delay differential equations

Nor Atirah Izzah Zulkefli, Normah Maan

Abstract


Delay differential equations (DDEs) arise many different phenomena including in physics, biology and chemistry. In many cases of the modeling of real world problems, information about the behaviour of a dynamical system is uncertain. In order to obtain a more realistic model, we have to take into account these uncertainties. Therefore, in this paper, we propose the existence and uniqueness theorems for fuzzy time-delay dynamical systems. We finally present some conclusions and new directions for further research in this area.


Keywords


Fuzzy Delay Differential Equation (FDDE); Fuzzy Time-Delay Dynamical Systems; Existence and Uniqueness Theorems|

Full Text:

PDF

References


A. J. Koshkouei and M. H. Farahi and K. J. Burnham, International Journal of Control, (to appear), 85 (2012) 147-158.

S. L. Chang and L.A. Zadeh, IEEE Transactions on Systems, Man and Cybernetics, 2 (1972) 330- 340.

D. Dubois and H. Prade, Fuzzy Sets and Systems, 8 (1982) 225-233.

A. Kandel and W. J. Byatt, Proceedings of the International Conference on Cybernetics and Society Tokyo, (1978) 1213-1216.

B. Bede and I. J. Rudas and A. L. Bencsik, Information Sciences, 177 (2007) 1648-1662.

T. Jayakumar and D. Maheskumar and K. Kanagarajan, Applied Mathemtical Sciences, 6 (2012) 2989-3002.

S. Song and Congxin Wu, Information Sciences, 108 (1998) 123-134.

J. Buckley and L. J. Jowers, Simulating Continuous Fuzzy Systems, (2006) 188.

L. J. Jowers and J. Buckley and K. D. Reilly, Information Sciences, 177 (2007) 436-448.

C. Xiaowei and Q. Zhongfeng, International Journal of Fuzzy

Systems, 13 (2011) 148-151.

K. Balachandran and P. Prakash, Journal of Korean Society for Industrial and Applied Mathematics, 6 (2002) 81-89.

V. Lupulescu and U. Abbas, Fuzzy Optim Decis Making, 11 (2012) 99–111.

R. D. Driver, Existence and Stability of Solutions of a Delay-

Differential System, Arch. Rational Mech. Anal., (1962).




DOI: https://doi.org/10.11113/mjfas.v10n3.280

Refbacks

  • There are currently no refbacks.


Copyright (c) 2014 Nor Atirah Izzah Zulkefli, Normah Maan

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Copyright © 2005-2020 Penerbit UTM Press, Universiti Teknologi Malaysia. Disclaimer: This website has been updated to the best of our knowledge to be accurate. However, Universiti Teknologi Malaysia shall not be liable for any loss or damage caused by the usage of any information obtained from this website.