Solving fuzzy differential equations by differential transformation method

Information Sciences

Volumn 179, Issue 7, 2009, Pages 956-966

  Allahviranloo, T ^a   Kiani, N A ^a   Motamedi, N ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Differential transformation method; Fuzzy differential equations; Fuzzy number; Fuzzy valued function; Generalized differentiability

Indexed keywords

BEAMS AND GIRDERS; CONFORMAL MAPPING; DIFFERENTIAL EQUATIONS; FUZZY RULES; FUZZY SETS; NUMERICAL METHODS;

DIFFERENTIAL TRANSFORMATION METHOD; FUZZY DIFFERENTIAL EQUATIONS; FUZZY NUMBER; FUZZY-VALUED FUNCTION; GENERALIZED DIFFERENTIABILITY;

NUMBER THEORY;

EID: 58349097540     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.11.016     Document Type: Article

References (33)

1. Abbod M.F., Linkens D.A., and Mahfof M. Survey of utilisation of fuzzy technology in medicine and healthcare. Fuzzy Sets and Systems 120 (2001) 331-349
2. 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
3. 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
4. Allahviranloo T., Ahmady N., and Ahmady E. Numerical solution of fuzzy differential equations by predictor-corrector method. Information Sciences 177 (2007) 1633-1647
5. Bede B., and Gal S.G. Almost Periodic fuzzy-number valued functions. Fuzzy Sets and Systems 147 (2004) 385-403
6. 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
7. Bede B., Imre J., Rudas C., and Attila L. First order linear fuzzy differential equations under generalized differentiability. Information Sciences 177 (2007) 3627-3635
8. 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.
9. Buckley J.J., and Feuring T. Fuzzy differential equations. Fuzzy Sets and System 110 (2000) 43-54
10. Chalco-Cano Y., and Roman-Flores H. On new solutions of fuzzy differential equations. Chaos, Solitons and Fractals (2006) 1016-1043
11. Chang S.L., and Zadeh L.A. On fuzzy mapping and control. IEEE Transactions on Systems, Man and Cybernetics 2 (1972) 30-34
12. Chen C.K., and Ho S.H. Solving partial differential equations by two-dimensional differential transform method. Applied Mathematics and Computation 106 (1999) 171-179
13. 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
14. Datta D.P., and mean T.g. scale free extension of real number system, fuzzy sets and i/f spectrum in physics and biology. Chaos, Solitons and Fractals 17 (2003) 781-788
15. Dubois D., and Prade H. Towards fuzzy differential calculus: Part 3, differentiation. Fuzzy Sets and Systems 8 (1982) 225-233
16. Fei W. Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients. Information Sciences 177 (2007) 4329-4337
17. 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
18. Goetschel R., and Voxman W. Elementary fuzzy calculus. Fuzzy sets and Systems 18 (1986) 31-43
19. Jang M.J., Chen C.L., and Liy Y.C. On solving the initial-value problems using the differential transformation method. Applied Mathematics and Computation 115 (2000) 145-160
20. Kaleva O. Fuzzy differential equations. Fuzzy Sets and Systems 24 (1987) 301-317
21. Kaleva O. The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35 (1990) 389-396
22. Lopez R.R. Comparison results for fuzzy differential equations. Information Sciences 178 (2008) 1756-1779
23. Ma M., Friedman M., and Kandel A. Numerical Solutions of fuzzy differential equations. Fuzzy Sets and Systems 105 (1999) 133-138
24. Mizukoshi M.T., Barros L.C., Chalco-Cano Y., Romàn-Flores H., and Bassanezi R.C. Fuzzy differential equations and the extension principle. Information Sciences 177 (2007) 3627-3635
25. El Nachie M.S. On a fuzzy Kahler manifold which is consistent with slit experiment. International Journal of Nonlinear Science and Numerical Simulation 6 (2005) 95-98
26. El Nachie M.S. From experimental quantum optics to quantity gravity via a fuzzy Kahler manifold. Chaos, Solitons and Fractals 25 (2005) 969-977
27. 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
28. Puri M.L., and Ralescu D.A. Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications 91 (1983) 552-558
29. Seikkala S. On the fuzzy initial value problem. Fuzzy Sets and Systems 24 (1987) 319-330
30. Wu C., and Gong Z. On Henstock integral of fuzzy-number-valued functions I. Fuzzy Sets and Systems 120 (2001) 523-532
31. Zadeh L. Toward a generalized theory of uncertainty (GTU) an outline. Information Sciences 172 (2005) 140
32. Zhang H., Liao X., and Yu J. Fuzzy modeling and synchronization of hyperchaotic systems. Chaos, Solitons and Fractals 26 (2005) 835-843
33. Zhou J.K. Differential Transformation and its Applications for Electrical Circuits (1986), Huarjung University Press