Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30320
Strict Stability of Fuzzy Differential Equations with Impulse Effect

Authors: Bhanu Gupta, Sanjay K.Srivastava

Abstract:

In this paper some results on strict stability heve beeb extended for fuzzy differential equations with impulse effect using Lyapunov functions and Razumikhin technique.

Keywords: lyapunov function, fuzzy differential equations, strict stability, impulsive differential equations, Razumikhin technique

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335674

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1121

References:


[1] J. J. Buckley, and T. H. Feuring, " Fuzzy Differential Equations", Fuzzy sets and systems, 110, 2000, pp. 43-54.
[2] P. Balasubramaniam and S. Muralisankar, Existence and Uniqueness of a Fuzzy Solution for Nonlinear Neural Functional Differential Equations, Comput. Math. Appl., 42 (2001), 961-967.
[3] P. Diamond, "Stability and Periodicity in Fuzzy Differential Equations", IEEE Trans. Fuzzy Systems, 8, 2000, pp. 583-590.
[4] M. Guo, X. Xue, and R. Li, " Impulsive Functional Differential Inclusions and Fuzzy Population Models", Fuzzy Sets and Systems, 138, 2003, pp. 601-615.
[5] 0. Kaleva, " Fuzzy Differential Equations", Fuzzy Sets and Systems, 24, 1987, pp. 301-317.
[6] A. Kandel, and W. J. Byatt, Fuzzy Differential Equations, Proc. Internat. Conf. on Cybernetics and Society, Tokyo-Kyoto, Japan, November 3-7, 1978, pp. 1213-1216.
[7] A. Kandel, and W. J. Byatt, "Fuzzy Processes", Fuzzy Sets and Systems, 4, 1980, 117-152.
[8] V. Lakshmikantham, and R. N. Mohapatra, Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis Publishers, London, 2003.
[9] V. Lakshmikantham, and Y. Zhang, " Strict Practicle Stability of Delay Differential Equation", Appl. Math.Comput., 118, 2001, pp. 275-285.
[10] V. Lakshmikantham, and R. N. Mohapatra, (2001), Strict Stability of Differential Equation, Nonlinear Analysis, 46, pp. 915-921.
[11] V. Lupulescu, "On a Class of Fuzzy Functional Differential Equations", Fuzzy Sets and Systems, 160, 2009, pp. 1547-1562.
[12] S. K. Srivastava and B. Gupta, "Existence of Nonlinear Fuzzy Differ¬ential Equations with Impulses", JIMS (to appear).
[13] A. S. Vatsala, " Impulsive Hybrid Fuzzy Differential Equations", Facta Universitatis, 3(14), 2003, pp. 851-859.
[14] Y. Zhang, and J. Sun, "Strict Stability of Impulsive Functional Differ¬ential Equations", J. Math. Anal. Appl., 301, 2005, pp. 237-248.