The local existence of solutions for random fuzzy integro-differential equations under generalized H-differentiability

Journal of Intelligent and Fuzzy Systems

Volumn 26, Issue 6, 2014, Pages 2701-2717

  Vu, Ho ^a   Hoa, No Van ^a   Phu, Nguyen Dinh ^b  

^a University of Ton Duc Thang   (Viet Nam)

^b UNIVERSITY OF NATURAL SCIENCES   (Viet Nam)

Author keywords

generalized Hukuhara derivative; Random fuzzy; random fuzzy differential equations; random fuzzy integro differential equations

Indexed keywords

INTEGRODIFFERENTIAL EQUATIONS;

FUZZY DIFFERENTIAL EQUATIONS; H-DIFFERENTIABILITY; INITIAL CONDITIONS; LOCAL EXISTENCE; RANDOM FUZZY;

DIFFERENTIAL EQUATIONS;

EID: 84901799529     PISSN: 10641246     EISSN: 18758967     Source Type: Journal    
DOI: 10.3233/IFS-130940     Document Type: Article

References (36)

1. T. Allahviranloo, S. Hajighasemi, M. Khezerloo, M. Khorasany and S. Salahshour, Existence and uniqueness of solutions of fuzzy volterra integro-differential equations, IPMU 2010, Part II, CCIS 81 (2010), 491-500
2. T. Allahviranloo, A. Amirteimoori, M. Khezerloo and S. Khezerloo, A new method for solving fuzzy volterra integrodifferential equations, Australian Journal of Basic and Applied Sciences 5 (2011), 154-164
3. T. Allahviranloo, S. Abbasbandy, O. Sedaghatfar and P. Darabi, A new method for solving fuzzy integro-differential equation under generalized differentiability, J Neural Computing and Applications 21 (2012), 191-196
4. T. Allahviranloo, M. Ghanbari, E. Haghi, A. Hosseinzadeh and R. Nouraei, A note on "Fuzzy linear systems", in Journal of Fuzzy Sets and Systems 177 (2011), 87-92
5. T. Allahviranloo and S. Gholami, Note on Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Journal of Fuzzy Set Valued Analysis 2012 (2012), 1-4
6. B. Bede and S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems 151 (2005), 581-599 (Pubitemid 40305079)
7. B. Bede, A note on "Two-point boundary value problems associated with non-linear fuzzy differential equations", Fuzzy Sets and Systems 157 (2006), 986-989
8. L. C. Barros, R. C. Bassanezi and P. A. Tonelli, Fuzzy modeling in population dynamics, Ecological Modeling 128 (2000), 27-33
9. J. J. Buckley and T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems 110 (2000), 43-54
10. Y. Chalco-Cano and H. Román-Flores, On new solutions of fuzzy differential equations, Chaos Solitons Fractals 38 (2008), 112-119 (Pubitemid 351503972)
11. Y. Chalco-Cano, A. Rufián-Lizana, H. Román-Flores, M. D. Jiménez-Gamero, Calculus for interval-valued functions using generalized Hukuhara derivative and applications, Fuzzy Sets and Systems (2012). In press
12. S. S. L. Chang and L. Zadeh, On fuzzy mapping and control, IEEE Transactions on System, Man and Cybernetics 2 (1972), 30-34
13. A. Colubi, J. S. Domínguez-Menchero, M. López-Díaz and D. A. Ralescu, A DE[0,1] representation of random upper semicontinuous functions, Proc Amer Math Soc 130 (2002), 3237-3242
14. D. Dubois and H. Prade, Towards fuzzy differential calculus, Fuzzy Sets and Systems 8 (1982), 225-233
15. W. Fei, Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coeffcients, Inform Sci 177 (2007), 4329-4337
16. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), 301-317
17. A. Khastan, J. J. Nieto and R. Rodriguez-Lopez, Variation of constant formula for first order fuzzy differential equations, Fuzzy Sets Syst 177 (2011), 20-33
18. E. P. Klement, M. L. Puri and D. A. Ralescu, Limit theorems for fuzzy random variables, Proc Roy Soc Lond A 407 (1986), 171-182
19. R. Kruse and K. D. Meyer Statistics with Vague Data, Kluwer, Dordrecht, 1987
20. H. Kwakernaak, Fuzzy random variables. Part I: Definitions and theorems, Inform Sci 15 (1978), 1-29
21. V. Lakshmikantham and Mohapatra, Theory of fuzzy differential equations and inclusions, Taylor Francis, London, 2003
22. V. Lakshmikantham and S. Leela, Fuzzy differential systems and the new concept of stability, J Nonlinear Dynamics and Systems Theory 1 (2001), 111-119
23. V. Lupulescu, On a class of fuzzy functional differential equations, Fuzzy Sets and Systems 160 (2009), 1547-1562
24. M. T. Malinowski, Interval differential equations with a second type Hukuhara derivative, Applied Mathematics Letters 24 (2011), 2118-2123
25. M. T. Malinowski, Random fuzzy differential equations under generalized Lipschitz condition, Nonlinear Analysis: Real- World Applications 13 (2012), 860-881
26. M. T. Malinowski, Existence theorems for solutions to random fuzzy differential equations, Nonlinear Analysis: Theory,Methods & Applications 73 (2010), 1515-1532
27. M. T. Malinowski, On random fuzzy differential equations, Fuzzy Sets and Systems 160 (2009), 3152-3165
28. M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Román- Flores and R. C. Bassanezi, Fuzzy differential equations and the extension principle, Information Sciences 177 (2007), 3627-3635 (Pubitemid 46920529)
29. J. A. Oguntuase, On an inequality of Gronwall, Journal of Inequalities in Pure and Applied Mathematics 2 (2001)
30. M. L. Puri and D. A. Ralescu, The concept of normality for fuzzy random variables, Ann Probab 13 (1985), 1373-1379
31. M. L. Puri and D. A. Ralescu, Fuzzy random variables, J Math Anal Appl 114 (1986), 409-422
32. M. L. Puri and D. Ralescu, Differential for fuzzy function, Journal of Mathematical Analysis and Applications 91 (1983), 552-558
33. S. Song and C. Wu, Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems 110 (2000), 55-67
34. L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal 71 (2009), 1311-1328
35. P. Terán Agraz, On Borel measurability and large deviations for fuzzy random variables, Fuzzy Sets and Systems 157 (2006), 2558-2568 (Pubitemid 44301497)
36. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.