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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 4

Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function

Ömer Akın
Tahir Khaniyev
Selami Bayeğ
Burhan Türkşen
Pages
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Publication Date
2016-07-13
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we illustrate some examples using the proposed algorithm.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we reformulate the algorithm in [7] to find an analytical expression for -cuts of the solution of the second order nonhomogeneous fuzzy initial value problem with fuzzy initial values and fuzzy forcing terms.
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Key Findings & Data:Firstly, we apply Zadeh’s Extension Principle to fuzzify the crisp initial value problem.
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Conclusion & Impact:Finally, we illustrate some examples using the proposed algorithm.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Fuzzy initial value problem · fuzzy forcing function · Zadeh’s extension principle

Abstract

In this paper, we reformulate the algorithm in [7] to find an analytical expression for -cuts of the solution of the second order nonhomogeneous fuzzy initial value problem with fuzzy initial values and fuzzy forcing terms. Firstly, we apply Zadeh’s Extension Principle to fuzzify the crisp initial value problem. Then, we use the Heaviside function and obtain the analytical form of -cuts of the solution of the fuzzy initial value problem. Finally, we illustrate some examples using the proposed algorithm.

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Cite This Article

Akın, Ö., Khaniyev, T., Bayeğ, S., Türkşen, B. (2016). Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function. Turkish Journal of Mathematics and Computer Science, Volume: 4. https://ajindex.com/articles/1324974

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References (20)

  1. Akın, Ö., Khaniyev, T., Oruç Ö., Türkşen, I. B., An algorithm for the solution of second order fuzzy initial value problems, Expert Syst. Appl., 40(2013), 953–957.
  2. Allahviranloo, T., Nejatbakhsh, Y., Shafeei, M., A note on ”Fuzzy di erential equations and the extension principle”, Journal of Information Science, 179(2009), 2049–2051.
  3. Bahrami, F., Ivaz, K., Khastan, A., New results on multiple solutions for n-th order fuzzy di erential equations under generalized di erentiability, Boundary Value Problems, 2009(2009), Article ID 395714, 13 pages.
  4. Banerjee, S., Mondal, S. P., Roy, T. K., First Order Linear Homogeneous Ordinary Di erential Equation in Fuzzy Environment, Int. J. Pure Appl. Sci. Technol., 14(2013), 16–26.
  5. Bede, B., Gal, S., Generalizations of the di erentiability of fuzzy number valued functions with applications to fuzzy di erential equation, Fuzzy Sets and Systems, 151(2005), 581–599.
  6. Bede, B., Bencsik, A., Rudas, I., First order linear fuzzy di erential equations under generalized di erentiability, Information Sciences, 177(2007), 1648–1662.
  7. Buckley, J. J., Feuring, T., Fuzzy initial value problem for N-th order linear di erential equations, Fuzzy Sets and Systems, 121(2001), 247–255.
  8. Byatt,W. J., Kandel, A., Fuzzy di erential equations, In Proceedings of the International Conference on Cybernetics and Society, Tokyo, Japan, 1978.
  9. Congxin, W., Shiji, S., Existence theorem to the Cauchy problem of fuzzy di erential equations under compactness-type conditions, Inf. Sci., 14(1998), 123–134.
  10. Ding, Z., Kandel, A., Ma M., Existence of the solutions of fuzzy di erential equations with parameters, Inf. Sci., 99(1997), 205–217.
  11. Gasilov, N., Amrahov, S. E., Fatullayev, A. G., A geometric approach to solve fuzzy linear systems of di erential equations, Applied Mathematics and Information Sciences, 5(2011), 484–499.
  12. Gasilov, N., Hashimoglu, I. F., Amrahov, S. E., Fatullayev, A. G., A New Approach to Non-Homogeneous Fuzzy Initial Value Problem, CMES-Computer Modeling in Engineering & Sciences, 85(2012), 367–378.
  13. Gasilov, N., Fatullayev, A. G., Amrahov, S. E., Khastan, A., A new approach to fuzzy initial value problem, Soft Computing, 18(2014), 217–225.
  14. H¨ullermeier, E., An approach to modelling and simulation of uncertain dynamical systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(1997), 117–137.
  15. Kaleva, O., Fuzzy di erential equations, Fuzzy Sets and Systems, 24(1987), 301–317.
  16. Oberguggenberger, M., Pittschmann, S., Di erential equations with fuzzy parameters, Mathematical and Computer Modelling of Dynamical Systems, 5(1999), 181–202.
  17. Puri, M., Ralescu, D., Di erential of fuzzy functions, Journal of Mathematical Analysis and Applications, 91(1983), 552–558.
  18. Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets Syst., 24(1987), 319–330.
  19. Zadeh, L. A., Fuzzy sets, Information and Control, 8(1965), 338–353.
  20. Zarei, H, Kamyad, A. V., Heydari, A. A., Fuzzy modeling and control of HIV infection, Comput. Math. Methods Med., 2012(2012), Article ID 893474, 17 pages.