Toward the existence and uniqueness of solutions of second-order fuzzy differential equations

Information Sciences

Volumn 179, Issue 8, 2009, Pages 1207-1215

  Allahviranloo, T ^a   Kiani, N A ^a   Barkhordari, M ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Fuzzy number; Fuzzy valued function; Generalized differentiability; H difference; Second order fuzzy differential equations

Indexed keywords

CONFORMAL MAPPING; DIFFERENTIAL EQUATIONS; FUZZY RULES; FUZZY SETS; PROBABILITY DENSITY FUNCTION;

FUZZY NUMBER; FUZZY-VALUED FUNCTION; GENERALIZED DIFFERENTIABILITY; H-DIFFERENCE; SECOND-ORDER FUZZY DIFFERENTIAL EQUATIONS;

DIFFERENCE EQUATIONS;

EID: 59349083165     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.11.004     Document Type: Article

References (27)

1. Abbasbandy S., Allahviranloo T., Lopez-Pouso O., and Nieto J.J. Numerical methods for fuzzy differential inclusions. Journal of Computer and Mathematics with Applications 48 (2004) 1633-1641
2. Abbasbandy S., and Allahviranloo T. Numerical solutions of fuzzy differential equations by Taylor method. Journal of Computational Methods in Applied Mathematics 2 (2002) 113-124
3. Allahviranloo T., Ahmady N., and Ahmady E. Numerical solution of fuzzy differential equations by predictor-corrector method. Information Sciences 177 (2007) 1633-1647
4. Bede B., and Gal S.G. Almost Periodic fuzzy-number valued functions. Fuzzy Sets and Systems 147 (2004) 385-403
5. Bede B., and Gal S.G. Generalizations of differentiablity of fuzzy number valued function with application to fuzzy differential equations. Fuzzy Sets and Systems 151 (2005) 581-599
6. Bede B., Rudas I.J., and Attila L. First order linear fuzzy differential equations under generalized differentiability. Information Sciences 177 (2007) 3627-3635
7. A. Bencsik, B. Bede, J. Tar, J. Fodor, Fuzzy differential equations in modeling hydraulic differential servo cylinders, in: Third Romanian-Hungarian Join Symposium on Applied Computational Intelligence(SACI), Timisoara, Romania, 2006.
8. Buckley J.J., and Feuring T. Fuzzy differential equations. Fuzzy Sets and Systems 110 (2000) 43-54
9. Chalco-Cano Y., and Roman-Flores H. On new solutions of fuzzy differential equations. Chaos, Solitons and Fractals (2006) 1016-1043
10. Chang S.L., and Zadeh L.A. On fuzzy mapping and control. IEEE Transaction on Systems Man Cybernetics 2 (1972) 30-34
11. Congxin W., and Shiji S. Exitance theorem to the Cauchy problem of fuzzy differential equations under compactance-type conditions. Information Science 108 (1993) 123-134
12. Dubois D., and Prade H. Towards fuzzy differential calculus: Part 3, Differentiation. Fuzzy Sets and Systems 8 (1982) 225-233
13. Fei W. Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients. Information Sciences 177 (2007) 4329-4337
14. Gal S.G. Approximation theory in fuzzy setting. In: Anastassiou G.A. (Ed). Handbook of Analytic-Computational Methods in Applied Mathematics (2000), Chapman Hall, CRC Press 617-666
15. Georgiou D.N., Nieto J.J., and Rodriguez-Lopez R. Initial value problems for higher-order fuzzy differential equations. Nonlinear Analysis 63 (2005) 587-600
16. Georgiou D.N., and Kougias I.E. On Cauchy problems for fuzzy differential equations. International Journal of Mathematical Science 15 (2004) 799-805
17. Goetschel R., and Voxman W. Elementary fuzzy calculus. Fuzzy Sets and Systems 18 (1986) 31-43
18. Kaleva O. Fuzzy differential equations. Fuzzy Sets and Systems 24 (1987) 301-317
19. Kaleva O. The Cauchy problem for Fuzzy differential equations. Fuzzy Sets and Systems 35 (1990) 389-396
20. Lopez R.R. Comparison results for fuzzy differential equations. Information Sciences 178 (2008) 1756-1779
21. Ma M., Friedman M., and Kandel A. Numerical Solutions of fuzzy differential equations. Fuzzy Sets and Systems 105 (1999) 133-138
22. Mizukoshi M.T., Barros L.C., Chalco-Cano Y., Román-Flores H., and Bassanezi R.C. Fuzzy differential equations and the extension principle. Information Sciences 177 (2007) 3627-3635
23. Papaschinopoulos G., Stefanidou G., and Efraimidi P. Existence, uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument. Information Sciences 177 (2007) 3855-3870
24. Puri M.L., and Ralescu D.A. Differentials of fuzzy functions. Journal of Mathematical Analysis and Application 91 (1983) 552-558
25. Seikkala S. On the fuzzy initial value problem. Fuzzy Sets and Systems 24 (1987) 319-330
26. Wu C., and Gong Z. On Henstock integral of fuzzy-number-valued functions I. Fuzzy Sets and Systems 120 (2001) 523-532
27. Zadeh L. Toward a generalized theory of uncertainty (GTU) - an outline. Information Sciences 172 (2005) 1-40