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Qualitative Analysis of Symmetric Fuzzy Stochastic Differential Equations Cover

Qualitative Analysis of Symmetric Fuzzy Stochastic Differential Equations

Open Access
|Sep 2025

References

  1. Arhrrabi, E., Elomari, M., Melliani, S. and Chadli, L.S. (2021). Existence and stability of solutions of fuzzy fractional stochastic differential equations with fractional Brownian motions, Advances in Fuzzy Systems 2021(4): 3948493.
  2. Arnold, L. (1974). Stochastic Differential Equations: Theory and Applications, John Wiley & Sons, New York.
  3. Arshad, H.M. and Shafqat, R. (2022). Approximating solutions of fuzzy stochastic fractional integro-evolution equations with the averaging principle: theory and applications, International Journal of Advancements in Mathematics 2(2): 150–163.
  4. Atyia, O.M., Fadhel, F.S. and Alobaidi, M.H. (2023). About the existence and uniqueness theorem of fuzzy random ordinary differential equations, Al-Nahrain Journal of Science 26(2): 30–35.
  5. Bandyopadhyay, A. and Kar, S. (2019). On fuzzy type-1 and type-2 stochastic ordinary and partial differential equations and numerical solution, Soft Computing 23: 3803–3821.
  6. Berger, M. and Schwarz, H. (1995). Logical valuation of connectives for fuzzy control by partial differential equations, International Journal of Applied Mathematics and Computer Science 5(4): 597–614.
  7. Feng, Y. (1999). Mean-square integral and differential of fuzzy stochastic processes, Fuzzy Sets and Systems 102(2): 271–280.
  8. Gihman, I.I. and Skorohod, A.V. (1972). Stochastic Differential Equations, Springer, Berlin.
  9. Gomes, L.T., de Barros, L.C. and Bede, B. (2015). Fuzzy Differential Equations in Various Approaches, Springer, Cham.
  10. Jackowska-Zduniak, B. (2022). Stochastic models of the slow/fast type of atrioventricular nodal reentrant tachycardia and tachycardia with conduction aberration, International Journal of Applied Mathematics and Computer Science 32(3): 429–440, DOI: 10.34768/amcs-2022-0031.
  11. Jafari, H. and Farahani, H. (2023). An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion, Stochastics and Dynamics 23(3): 2350017.
  12. Jafari, H. and Malinowski, M.T. (2023). Symmetric fuzzy stochastic differential equations driven by fractional Brownian motion, Symmetry 15(7): 1436.
  13. Kaleva, O. (1987). Fuzzy differential equations, Fuzzy Sets and Systems 24(3): 301–317.
  14. Kloeden, P.E. and Platen, E. (1992). Numerical Solution of Stochastic Differential Equations, Springer, Berlin/Heidelberg.
  15. Lee, H., Stannat, W. and Trutnau, G. (2022). Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients, Springer, Singapore.
  16. Long, H.V. (2018). On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability, Computational and Applied Mathematics 37: 2738–2765.
  17. Luo, D., Wang, X., Caraballo, T. and Zhu, Q. (2023). Ulam–Hyers stability of Caputo-type fractional fuzzy stochastic differential equations with delay, Communications in Nonlinear Science and Numerical Simulation 121: 107229.
  18. Malinowski, M.T. (2009). On random fuzzy differential equations, Fuzzy Sets and Systems 160(21): 3152–3165.
  19. Malinowski, M.T. (2012a). Itô type stochastic fuzzy differential equations with delay, Systems and Control Letters 61(6): 692–701.
  20. Malinowski, M.T. (2012b). Strong solutions to stochastic fuzzy differential equations of Itô type, Mathematical and Computer Modelling 55(3–4): 918–928.
  21. Malinowski, M.T. (2013). Some properties of strong solutions to stochastic fuzzy differential equations, Information Sciences 252: 62–80.
  22. Malinowski, M.T. (2014). Fuzzy and set-valued stochastic differential equations with local Lipschitz condition, IEEE Transactions on Fuzzy Systems 23(5): 1891–1898.
  23. Malinowski, M.T. (2016a). Bipartite fuzzy stochastic differential equations with global Lipschitz condition, Mathematical Problems in Engineering 2016(3): 1–13.
  24. Malinowski, M.T. (2016b). Stochastic fuzzy differential equations of a nonincreasing type, Communications in Nonlinear Science and Numerical Simulation 33: 99–117.
  25. Malinowski, M.T. (2020). Symmetric fuzzy stochastic differential equations with generalized global Lipschitz condition, Symmetry 12(5): 819.
  26. Mazandarani, M. and Xiu, L. (2021). A review on fuzzy differential equations, IEEE Access 9: 62195–62211.
  27. Ogura, Y. (2008). On stochastic differential equations with fuzzy set coefficients, Soft Methods for Handling Variability and Imprecision, Springer, Berlin, pp. 263–270.
  28. Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications, Springer, Berlin.
  29. Pedro, F.S., Lopes, M.M., Wasques, V.F., Esmi, E. and de Barros, L.C. (2023). Fuzzy fractional differential equations with interactive derivative, Fuzzy Sets and Systems 467: 108488.
  30. Priyadharsini, J. and Balasubramaniam, P. (2020). Existence of fuzzy fractional stochastic differential system with impulses, Computational and Applied Mathematics 39: 195.
  31. Sarhan, F.H. and Ismail, H.K. (2023). Approximation solutions of backward fuzzy stochastic differential equations, International Journal of Mathematics and Computer Science 18(4): 647–654.
  32. Srivastava, H.M., Chaharpashlou, R., Saadati, R. and Li, C. (2022). A fuzzy random boundary value problem, Axioms 11)(8): 414.
  33. Taniguchi, T. (1992). Successive approximations to solutions of stochastic differential equations, Journal of Differential Equations 96(1): 152–169.
  34. Vu, H. (2017). Random fuzzy differential equations with impulses, Complexity 2017: 4056016.
  35. Wen, X., Malinowski, M.T., Li, H., Liu, H. and Li, Y. (2024). Numerical solution of fuzzy stochastic Volterra integral equations with constant delay, Fuzzy Sets and Systems 493: 109098.
  36. Xia, S., Chen, L., Liu, S. and Yang, H. (2022). A new method for decision making problems with redundant and incomplete information based on incomplete soft sets: From crisp to fuzzy, International Journal of Applied Mathematics and Computer Science 32(4): 657–669, DOI: 10.34768/amcs-2022-0045.
  37. Yamada, T. (1981). On the successive approximations of solutions of stochastic differential equations, Journal of Mathematics of Kyoto University 21(3): 501–515.
  38. Zadeh, L.A. (1965). Fuzzy sets, Information and Control 8: 338–353.
  39. Zadeh, L.A. (2002). From computing with numbers to computing with words—From manipulation of measurements to manipulation of perception, International Journal of Applied Mathematics and Computer Science 12(3): 307–324.
  40. Zhang, J. (2008). Set-valued stochastic integrals with respect to a real valued martingale, in D. Dubois et al. (Eds), Soft Methods for Handling Variability and Imprecision, Springer, Berlin, pp. 253–259.
DOI: https://doi.org/10.61822/amcs-2025-0028 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 403 - 416
Submitted on: Dec 31, 2024
Accepted on: May 4, 2025
Published on: Sep 8, 2025
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Marek T. Malinowski, published by University of Zielona Góra
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