Değişken Katsayılı İkinci-Mertebe Fuzzy Diferansiyel Denklem

Year 2024, , 272 - 280, 15.03.2024

Hülya Gültekin Çitil

https://doi.org/10.31466/kfbd.1401325

Abstract

Bu çalışma, değişken katsayılı ikinci-mertebe fuzzy diferansiyel denklem için bir fuzzy başlangıç değer problemi üzerinedir. Problemin çözümü fuzzy Laplace dönüşüm yöntemi ile çözülmüştür. Problemi açıklamak için örnek verilmiştir. Problemi yorumlamak ve sonuçları görmek için, her bir alfa seviye seti için problemin grafikleri çizilmiştir.

Keywords

Fuzzy diferansiyel denklem, Fuzzy fonksiyon, Fuzzy problem

Second-Order Fuzzy Differential Equation with Variable Coefficients

Abstract

This paper is on a fuzzy initial value problem for second-order fuzzy differential equation with variable coefficients. The solution of the problem is solved via fuzzy Laplace transform method. Example is given to illustrate the problem. To interpret the problem and see the results, the graphics of the problem are drawn for each alpha level set.

Keywords

Fuzzy differential equation, Fuzzy function, Fuzzy problem

References

• Allahviranloo T. and Barkhordari Ahmadi M. (2010). Fuzzy Laplace transforms, Soft Computing, 14(3), 235–243.
• Akın Ö., Khaniyev T., Bayeğ S. and Türkşen B. (2016), Solving a se-cond order fuzzy initial value problem using the heaviside function, Turkish Journal of Mathematics and Computer Science, 4, 16–25.
• Bede B. and Gal S. G. (2005). Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151, 581–599.
• Bede B., Rudas I. J. and Bencsik A. L. (2007), First order linear fuzzy differential equations under generalized differentiability, Information Sciences, 177, 1648–1662.
• Belhallaj Z., Melliani S., Elomari M. and Chadli L. S. (2023). Application of the intuitionistic fuzzy Laplace transform method for resolution of one dimensional wave equations, International Journal of Difference Equations, 18(1), 211-225.
• Buckley J. J. and Feuring T. (2000). Fuzzy differential equations, Fuzzy Sets and Systems 110, 43-54.
• Eljaoui E. and Melliani S. (2023). A study of some properties of fuzzy Laplace transform with their applications in solving the second-order fuzzy linear partial differential equations, Advances in Fuzzy Systems, 2023 Article ID 7868762, 1-15.
• Hüllermeier E. (1997). An approach to modelling and simulation of uncertain dynamical systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5, 117–137.
• Gültekin Çitil H. (2018). The relationship between the solutions according to the noniterative method and the generalized differentiability of the fuzzy boundary value problem, Malaya Journal of Matematik, 6(4) 781-787.
• Gültekin Çitil H. (2019), Comparisons of the exact and the approximate solutıons of second-order fuzzy linear boundary value problems, Miskolc Mathematical Notes, 20(2) 823–837.
• Gültekin Çitil H. (2020). On third-order fuzzy differential equations by fuzzy Laplace transform, J. BAUN Inst. Sci. Technol., 22(1), 345-353.
• Gültekin Çitil H. (2020). The problem with fuzzy eigenvalue parameter in one of the boundary conditions, An International Journal of Optimization and Control: Theories & Applications, 10(2), 159-165.
• Gültekin Çitil H. (2020). Solutions of fuzzy differential equation with fuzzy number coefficient by fuzzy Laplace transform, Comptes rendus de l’Acad´emie bulgare des Sciences, 73(9), 1191-1200.
• Jafaria R., Yub W., Razvarzb S. and. Gegovc A. (2021). Numerical methods for solving fuzzy equations: A survey, Fuzzy Sets and Systems, 404, 1–22.
• Khastan A. and Nieto J. J. (2010). A boundary value problem for second order fuzzy differential equations, Nonlinear Analysis, 72 (9-10), 3583-3593.
• Nieto J. J., Rodríguez-López R., Franco D. (2006). Linear first-order fuzzy differential equation, International Journal of Uncertainty Fuzziness Knowledge-Based Systems, 14, 687-709.
• Nieto J. J., Khastan A. and. Ivaz K. (2009). Numerical solution of fuzzy differential equations under generalized differentiability, Nonlinear Analysis: Hybrid Systems, 3, 700-707.
• Patel K. R. and Desai N. B. (2017). Solution of fuzzy initial value problems by fuzzy Laplace transform, Kalpa Publications in Computing, 2, 25-37.
• Patel K. R., Desai N. B. (2017). Solution of variable coefficient fuzzy differential equations by fuzzy Laplace transform, International Journal on Recent and Innovation Trends in Computing and Communication, 5(6), 927-942.
• Samuel M. Y. and Tahir A. (2021). Solution of first order fuzzy partial differential equations by fuzzy Laplace transform method, Bayero Journal of Pure and Applied Sciences, 14(2), 37 – 51.
• Saqib M., Akram M., Bashir S. and Allahviranloo T. (2021). Numerical solution of bipolar fuzzy initial value problem, Journal of Intelligent & Fuzzy Systems, 40(1), 1309-1341.