A study on two fourth-order fuzzy problems with fuzzy coefficients

Abstract

This study is on the solutions of two fourth-order fuzzy problems with positive and negative fuzzy number coefficients. The solutions are found using the fuzzy Laplace transform method. Main results are given. Two examples are solved to illustrate the problems. Graphics of the found solutions are drawn for alpha level sets. Also, the graphics are interpreted and conclusions are given.

Keywords

• Fourth-order fuzzy problem
• fuzzy function
• fuzzy Laplace transform method

Fuzzy katsayılı iki dördüncü-mertebeden fuzzy problem üzerine bir çalışma

Abstract

Bu çalışma, pozitif ve negatif fuzzy sayı katsayılı iki dördüncü-mertebeden fuzzy problemin çözümleri üzerinedir. Çözümler fuzzy Laplace dönüşüm metodu kullanılarak bulundu. Temel sonuçlar verildi. Problemleri göstermek için iki örnek çözüldü. Alfa seviye setleri için bulunan çözümlerin grafikleri çizildi. Ayrıca, grafikler yorumlandı ve sonuçlar verildi.

Keywords

• Dördüncü-mertebe fuzzy problem
• fuzzy fonksiyon
• fuzzy Laplace dönüşüm metodu

References

1. Akin O., Khaniyev T., Oruc O., Turksen I.B., An algorithm for the solution of second order fuzzy initial value problems, Expert Systems with Applications, 40, 3, 953-957, (2013).
2. Akin O., Bayeg S., Intuitionistic fuzzy initial value problems-an application, Hacettepe Journal of Mathematics and Statistics, 48, 6, 1682-1694, (2019).
3. Allahviranloo T., Hooshangian L., A new method to find fuzzy nth order derivation and applications to fuzzy nth order arithmetic based on generalized h-derivation, An International Journal of Optimization and Control: Theories & Applications, 4, 2, 105-121, (2014).
4. Bayeg S., Mert R., Akin O., Khaniyev T., On a type-2 fuzzy approach to solution of second-order initial value problem, Soft Computing, 26, 4, 1671-1683, (2022).
5. Gasilov N., Amrahov S. E., Fatullayev A. G., Solution of linear differential equations with fuzzy boundary values, Fuzzy Sets and Systems, 257, 169–183, (2014).
6. Gasilov N., Amrahov S. E., Fatullayev A. G., A geometric approach to solve fuzzy linear systems of differential equations, Applied Mathematics and Information Sciences, 5, 3, 484-499, (2011).
7. Gültekin Çitil H., Comparison results of linear differential equations with fuzzy boundary values, Journal of Science and Arts, 1, 42, 33-48, (2018).
8. Gültekin Çitil H., On a boundary value problem with fuzzy forcing function and fuzzy boundary values, International Journal of Mathematical Combinatorics 2, 1-16, (2021).

9. Gültekin Çitil H., 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, (2020).
10. Liu H.-K., Comparison results of two-point fuzzy boundary value problems, International Journal of Computational and Mathematical Sciences, 5, 1, 1-7, (2011).
11. Jafari R., Yu W., Razvarz S., Gegov A., Numerical methods for solving fuzzy equations: A survey, Fuzzy Sets and Systems 404, 1–22, (2021).
12. Khastan A., Nieto J. J., A boundary value problem for second order fuzzy differential equations, Nonlinear Analysis, 72, 9-10, 3583-3593, (2010).
13. Samuel M.Y., Tahir A., Solution of first order fuzzy partial differential equations by fuzzy Laplace transform method, Bayero Journal of Pure and Applied Sciences, 14, 2, 37-51, (2021).
14. Saqib M., Akram M., Bashir S., Allahviranloo T., Numerical solution of bipolar fuzzy initial value problem, Journal of Intelligent & Fuzzy Systems 40, 1, 1309-1341, (2021).
15. Sheergojri A. R., Iqbal P., Agarwal P., Ozdemir N., Uncertainty-based Gompertz growth model for tumor population and its numerical analysis, An International Journal of Optimization and Control: Theories & Applications, 12, 2, 137-150, (2022).
16. Allahviranloo T., Barkhordari Ahmadi M., Fuzzy Laplace transforms, Soft Computing, 14, 3, 235-243, (2010).
17. Allahviranloo T., Abbasbandy S., Salahshour S., Hakimzadeh A.,. A new method for solving fuzzy linear differential equations, Computing , 92, 181–197, (2011).
18. Gültekin Çitil H., On third-order fuzzy differential equations by fuzzy Laplace transform, J. BAUN Inst. Sci. Technol., 22, 1, 345-353, (2020).
19. Gültekin Çitil H., Solving the fuzzy initial value problem with negative coeffıcient by using fuzzy Laplace transform, Facta Universitatis, Series: Mathematics and Informatics, 35, 1, 201-215, (2020).
20. Gültekin Çitil H., On a fuzzy problem with variable coefficient by fuzzy Laplace transform, Journal of the Institute of Science and Technology, 10, 1, 576-583, (2020).
21. Muhammad Ali H. F., Haydar A. K., On fuzzy Laplace transforms for fuzzy differential equations of the third order, Journal of Kerbala University , 11, 3, 251-256, (2013).
22. Patel K. R., Desai N. B., Solution of fuzzy initial value problems by fuzzy Laplace transform, Kalpa Publications in Computing, 2, 25-37, (2017).
23. Patel K. R., Desai N. B., 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, (2017).
24. Salahshour S., Allahviranloo T., Applications of fuzzy Laplace transforms, Soft Computing, 17, 1, 145-158, (2013).
25. Ahmad L., Farooq M., Abdullah S., Solving fourth order fuzzy differential equation by fuzzy Laplace transform, Annals of Fuzzy Mathematics and Informatics, 12, 3, 449-468, (2016).