The Cauchy problem of fuzzy differential equations under generalized differentiability

Fuzzy Sets and Systems

Volumn 200, Issue , 2012, Pages 1-24

  Li, Jinxian ^a,b   Zhao, Aimin ^b   Yan, Jurang ^b  

^a SICHUAN UNIVERSITY   (China)

^b SHANXI UNIVERSITY   (China)

Author keywords

Analysis; Fuzzy set valued mapping; Generalized differentiability

Indexed keywords

ANALYSIS; CAUCHY PROBLEMS; DYNAMIC STUDIES; FUZZY DIFFERENTIAL EQUATIONS; GENERALIZED DIFFERENTIABILITY; H-DIFFERENTIABILITY; NEW SOLUTIONS; SET-VALUED MAPPING;

FUZZY SETS;

DIFFERENTIAL EQUATIONS;

EID: 84861102043     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2011.10.009     Document Type: Article

References (43)

1. C.V. Negoita, and D.A. Ralescu Applications of Fuzzy Sets to System Analysis 1975 Birkhauser Basel
2. P. Diamond, and P. Kloden Metric Spaces of Fuzzy Sets 1994 World Scientific Singapore
3. V. Lakshmikantham, T. Gnana Bhaskar, and J. Vasundhara Devi Theory of Set Differential Equations in Metric Spaces 2006 Cambridge Scientific Publishers
4. M. Hukuhara Intégration des applications mesurables dont la valeur est un compact convex Funkcial. Ekvac. 10 1967 205 229
5. D. Dubois, and H. Prade Towards fuzzy differential calculus. Part I. Integration of fuzzy mappings Fuzzy Sets Syst. 8 1982 1 17 (Pubitemid 14449709)
6. D. Dubois, and H. Prade Towards fuzzy differential calculus. Part II. Integration on fuzzy intervals Fuzzy Sets Syst. 8 1982 105 116 (Pubitemid 14449698)
7. M. Puri, and D. Ralescu Differentials of fuzzy functions J. Math. Anal. Appl. 91 1983 552 558
8. M.L. Puri, and D.A. Ralescu Differentials of fuzzy functions J. Math. Anal. Appl. 114 1986 409 422
9. O. Kaleva Fuzzy differential equations Fuzzy Sets Syst. 24 1987 301 317
10. S. Seikkala On the fuzzy initial value problem Fuzzy Sets Syst. 24 1987 319 330
11. C. Wu, S. Song, and E. Stanley Lee Approximate solutions, existence, and uniqueness of the Cauchy problem of fuzzy differential equations J. Math. Anal. Appl. 202 1996 629 644 (Pubitemid 126165689)
12. S. Song, and C. Wu Existence and uniqueness of solutions to the Cauchy problem of fuzzy differential equations Fuzzy Sets Syst. 110 2000 55 67
13. J.J. Buckley, and T.H. Feuring Fuzzy differential equations Fuzzy Sets Syst. 110 2000 43 54
14. M.T. Malinowski On random fuzzy differential equations Fuzzy Sets Syst. 160 2009 3152 3165
15. R.P. Agarwal, V. Lakshmikantham, and J.J. Nieto On the concept of solution for fractional differential equations with uncertainty Nonlinear Anal. Theory Methods Appl. 72 2009 2859 2862
16. S. Arshad, and V. Lupulescu On the fractional differential equations with uncertainty Nonlinear Anal. Theory Methods Appl. 74 2011 3685 3693
17. P. Prakash, G. Sudha Priya, and J.H. Kim Third-order three-point fuzzy boundary value problems Nonlinear Anal. Hybrid Syst. 3 2009 323 333
18. S. Pederson, and M. Sambandham Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem Inf. Sci. 179 2009 319 326
19. J. Xu, Z. Liao, and J.J. Nieto A class of linear differential dynamical systems with fuzzy matrices J. Math. Anal. Appl. 368 2010 54 68
20. B. Ghazanfari, S. Niazi, A.G. Ghazanfari, Linear matrix differential dynamical systems with fuzzy matrices, Appl. Math. Modelling, in press, doi: 10.1016/j.apm.2011.05.054.
21. D. Vorobiev, and S. Seikkala Toward the theory of fuzzy differential equations Fuzzy Sets Syst. 125 2002 231 237 (Pubitemid 33110361)
22. A. Bencsik, B. Bede, J. Tar, J. Fodor, Fuzzy differential equations in maleing hydraulic differential servo cylinders, in: Third Romain-Hungorian Joint Symposium on Applied Computational Intelligence (SACI), Timisoara, Romania, 2006.
23. J.J. Nieto, and R. Rodríguez-López Bounded solutions for fuzzy differential and integral equations Chaos Solitons Fractals 27 2006 1376 1386 (Pubitemid 41329831)
24. A.D.R. Choudary, and T. Donchev On Peano theorem for fuzzy differential equations Fuzzy Sets Syst. 177 2011 93 94
25. J.J. Nieto, R. Rodríguez-López, and D.N. Georgiou Fuzzy differential systems under generalized metric spaces approach Dyn. Syst. Appl. 17 2008 1 24
26. V. Lakshmikantham, and J.J. Nieto Differential equations in metric spaces: an introduction and an application to fuzzy differential equations Dyn. Continuous Discrete Impulsive Syst. Ser. A: Math. Anal. 10 2003 991 1000 (Pubitemid 39258664)
27. P. Diamond Stability and Periodicity in fuzzy differential equations IEEE Trans. Fuzzy Syst. 8 2000 583 590
28. V. Lakshnikantham, and A.A. Tolstonogov Existence and interrelation between set and fuzzy differential equations Nonlinear Anal. Theory Methods Appl. 55 2003 255 268
29. J.J. Buckley, and T. Feuring Introduction to fuzzy partial differential equations Fuzzy Sets Syst. 105 1999 241 248 (Pubitemid 129530669)
30. J.J. Buckley, and T. Feuring Fuzzy initial value problem for N -th order linear differential equations Fuzzy Sets Syst. 121 2001 247 255
31. Y. Chalco-Cano, and H. Román-Flores Comparison between some approaches to solve fuzzy differential equations Fuzzy Sets Syst. 160 2009 1517 1527
32. Y. Chalco-Cano, and H. Román-Flores On new solutions of fuzzy differential equations Chaos Solitons Fractals 38 2008 112 119 (Pubitemid 351503972)
33. B. Bede, I.J. Rudas, and A.L. Bencsik First order linear fuzzy differential equations under generalized differentiability Inf. Sci. 177 2007 1648 1662 (Pubitemid 46107427)
34. M.T. Malinowski Existence theorems for solutions to random fuzzy differential equations Nonlinear Anal. Theory Methods Appl. 73 2010 1515 1532
35. B. Bede, and S.G. Gal Almost periodic fuzzy-number-valued functions Fuzzy Sets Syst. 147 2004 385 403
36. B. Bede, and S.G. Gal Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations Fuzzy Sets Syst. 151 2005 581 599 (Pubitemid 40305079)
37. A. Khastan, and J.J. Nieto A boundary value problem for second order fuzzy differential equations Nonlinear Anal. Theory Methods Appl. 72 2010 3583 3593
38. J.J. Nieto, A. Khastan, and K. Ivaz Numerical solution of fuzzy differential equations under generalized differentiability Nonlinear Anal. Hybrid Syst. 3 2009 700 707
39. A. Khastan, J.J. Nieto, and R. Rodríuez-Lóez Variation of constant formula for first order fuzzy differential equations Fuzzy Sets Syst. 177 2011 20 33
40. L. Stefanini, and B. Bede Generalized Hukuhara differentiability of interval-valued functions and interval differential equations Nonlinear Anal. Theory Methods Appl. 71 2009 1311 1328
41. L. Stefanini A generalization of Hukuhara difference and division for interval and fuzzy arithmetic Fuzzy Sets Syst. 161 2010 1564 1584
42. Y. Chalco-Cano, H. Romá-Flores, and M.D. Jiménez-Gamero Generalized derivative and π-derivative for set-valued functions Inf. Sci. 181 2011 2177 2188
43. G.E. Ladas, and V. Lakshmikantham Differential Equations in Abstract Spaces 1972 Academic Press New York