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A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS

Heng-You Lan
영남수학회 (Youngnam Mathematical Society)|2008.01|East Asian Mathematical Journal|제24권 제1호|pp. 111-123

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참고문헌

키워드

fixed pointCauchy problemexistence and uniqueness
주제분류수학

초록

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

Abstract

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

참고문헌 (42)

  1. S. Abbasbandy, "Numerical methods for fuzzy differential inclusions", Comput. Math. Appl, 48, pp.1633~1641 (2004)
  2. R. P. Agarwal, "Viability theory and fuzzy differential equations", Fuzzy Sets and Systems, 151, pp.563~580 (2005)
  3. B. Bede, "First order linear fuzzy differential equations under generalized differentiability", Inform. Sci, 177, pp.1648~1662 (2007)
  4. Y. Chalco-Cano, "On new solutions of fuzzy differential equations", Chaos Solitons & Fractals
  5. S. S. L. Chang, "On fuzzy mapping and control", IEEE Trans. Systems Man Cybernet, 2, pp.30~34 (1972)
  6. M. Choisy, "Dynamics of infectious diseases and pulse vaccination: Teasing apart the embedded resonance effects", Physica D: Nonlinear Phenomena, 22, pp.26~35 (2006)
  7. J. V. Devi, "Method of vector Lyapunov functions for impulsive fuzzy systems", Dynam. Systems Appl, 13, pp.521~531 (2004)
  8. Y. P. Fang, "Iterative algorithm for a system of variational inclusions involving H-accretive operators in Banach spaces", Acta Math. Hungar, 108(3), pp.183~195 (2005)
  9. S. Gao, "Analysis of a delayed epidemic model with pulse vaccination and saturation incidence", Vaccine, 24, pp.6037~6045 (2006)
  10. D. N. Georgiou, "On Cauchy problems for fuzzy differential equations", Int. J. Math. Math. Sci, 15, pp.799~805 (2004)
  11. D. N. Georgiou, "Initial value problems for higherorder fuzzy differential equations", Nonlinear Analysis, 63, pp.587~600 (2005)
  12. T. Gnana Bhaskar, "Revisiting fuzzy differential equations", Nonlinear Anal, 58, pp.351~358 (2004)
  13. M. Guo, "Impulsive functional differential inclusions and fuzzy population models", Fuzzy Sets and Systems, 138, pp.601~615 (2003)
  14. S. Heikkil¨a, "Uniqueness and existence results for implicit impulsive differential equations", Nonlinear Anal, 42, pp.13~26 (2000)
  15. N. J. Huang, "Existence of the solution for a class of implicit differential equations in Banach spaces", Dyn. Contin. Discrete Impuls. Syst. Ser. A, 13, pp.27~36 (2006)
  16. G. Iovane, "Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions", Nonlinear Anal, 66, pp.498~508 (2007)
  17. O. Kaleva, "Fuzzy differential equations", Fuzzy Sets and Systems, 24, pp.301~317 (1987)
  18. O. Kaleva, "The Cauchy problem for fuzzy differential equations", Fuzzy Sets and Systems, 35, pp.389~396 (1990)
  19. O. Kaleva, "A note on fuzzy differential equations", Nonlinear Anal, 64, pp.895~900 (2006)
  20. P. E. Kloeden, "Remarks on Peano-like theorems for fuzzy differential equations", Fuzzy Sets and Systems, 44, pp.161~163 (1991)
  21. V. Lakshmikantham, "Basic results for fuzzy impulsive differential equations", Math. Ineq. Appl, 4(2), pp.239~246 (2001)
  22. V. Lakshmikantham, "Theory of Fuzzy Differential Equations and Inclusions" (2003), Taylor and Francis Publishers
  23. D. W. C. Ho, "Stability of Takagi-Sugeno fuzzy delay systems with impulse", IEEE Trans. Fuzzy Systems (2007)
  24. H. Y. Lan, "Nonlinear first order implicit fuzzy differential equations", Dyn. Contin. Discrete Impuls. Syst. Ser. B, 13, pp.353~356 (2006)
  25. H. Y. Lan, "First order nonlinear implicit impulsive integrodifferential equations in Banach spaces", Dyn. Contin. Discrete Impuls. Syst. Ser. A, 13, pp.803~813 (2006)
  26. W. Li, "Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics", J. Comput. Appl. Math, 174, pp.227~238 (2005)
  27. J. Li, "Impulsive periodic boundary value problems of first-order differential equations", J. Math. Anal. Appl, 325, pp.226~236 (2007)
  28. Yu. A. Mitropolskiy, "About a generalization of Bellman-Bihari type inequalities for discontinuous functions and their applications", Nonlinear Anal, 66, pp.2140~2165 (2007)
  29. J. J. Nieto, "The Cauchy problem for continuous fuzzy differential equations", Fuzzy Sets and Systems, 102, pp.259~262 (1999)
  30. J. J. Nieto, "Bounded solutions for fuzzy differential and integral equations", Chaos Solitons & Fractals, 27, pp.1376~1386 (2006)
  31. J. J. Nieto, "Linear first-order fuzzy differential equations", International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 14, pp.687~709 (2006)
  32. A. d’Onofrio, "pulse vaccination strategy in the SIR epidemic model with vertical transmission", Appl. Math. Lett, 18, pp.729~732 (2005)
  33. M. A. Rojas-Medar, "Fuzzy quasilinear spaces and applications", Fuzzy Sets and Systems, 152, pp.173~190 (2005)
  34. A. M. Samoilenko, "Impulsive Differential Equations" (1995), World Scientific
  35. S. J. Song, "Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations", Fuzzy Sets and Systems, 110, pp.55~67 (2000)
  36. L. Stefanini, "Parametric representation of fuzzy numbers and application to fuzzy calculus", Fuzzy Sets and Systems, 157, pp.2423~2455 (2006)
  37. S. Tang, "Density-dependent birth rate, birth pulses and their population dynamic consequences", J. Math. Biol, 44, pp.185~199 (2002)
  38. W. Wang, "The dynamic complexity of a three-species Beddingtontype food chain with impulsive control strategy", Chaos Solitons & Fractals, 32, pp.1772~1785 (2007)
  39. J. Yan, "Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems", Math. Comput. Model, 40, pp.509~518 (2004)
  40. Dynamic Impulse Systems: Theory and Applications, "S. T. Zavalishchin", Theory and Applications,Kluwer Academic Publishers Group,Dordrecht, ~ (1997)
  41. W. Zhang, "Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays", Math. Comput. Model, 39, pp.479~493 (2004)
  42. H. J. Zimmermann, "Fuzzy Set Theory and Its Applications" (1991), Kluwer Academic Publishers

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