On the foundation of solving a first-order weak fuzzy complex initial value problem (WFC-IVP)

Authors

https://doi.org/10.48313/uda.vi.81

Abstract

The aim of this paper is to introduce for the first time the basic concept of the first-order Weak Fuzzy Complex- Initial Value Problems (WFC-IVPs). We find, using a special isomorphic transformation function, that solving a WFC-IVP is equivalent to solving two classical real IVPs with respect to their own real variables. Thus, we study “the existence and uniqueness”, “the stability”, and “the well-posedness” associated with the WFC-IVPs in terms of definitions, lemmas, and theorems. Then, we get the approximate solutions of a WFC-IVP by stable and convergent numerical methods. One of the most famous and simple methods to solve IVPs is Euler’s method, which is discussed for well-posed WFC-IVPs. However, we focus on a stable linear model WFC-IVP with real coefficients and real initial values, and we further investigate the properties of the results. Additionally, we present an example with tables and diagrams of its numerical solutions and absolute errors by Python to clarify how Euler’s algorithm works.

Keywords:

Weak fuzzy complex set, Weak fuzzy complex functions, Initial value problem, Euler’s method

References

  1. [1] Hatip, A. (2023). An introduction to weak fuzzy complex numbers. Galoitica journal of mathematical structures and applications, 3(1), 8–13. https://doi.org/10.54216/GJMSA.030101
  2. [2] Hatip, A. (2023). On the fuzzy weak complex vector spaces. Galoitica: Journal of mathematical structures and applications, 3(1), 29–32. https://doi.org/10.54216/gjmsa.030105
  3. [3] Ali, R. (2023). On the weak fuzzy complex inner products on weak fuzzy complex vector spaces. Neoma journal of mathematics and computer science, 1. https://doi.org/10.5281/zenodo.7953682
  4. [4] Alhasan, Y. A., Alfahal, A. M. A., Abdulfatah, R. A., Nordo, G., & Zahra, M. M. A. (2023). On some novel results about weak fuzzy complex matrices. International journal of neutrosophic science, 21(1), 134–140. https://doi.org/10.54216/IJNS.210112
  5. [5] Abualhomos, M., Salameh, W. M. M., Bataineh, M., Al-Qadri, M. O., Alahmade, A., & Al-Husban, A. (2024). An effective algorithm for solving weak fuzzy complex diophantine equations in two variables. International journal of neutrosophic science, 23(4), 386–394. https://doi.org/10.54216/IJNS.230431
  6. [6] Alfahal, A. M. A., Abobala, M., Alhasan, Y. A., & Abdulfatah, R. A. (2023). Generating weak fuzzy complex and anti weak fuzzy complex integer solutions for pythagoras diophantine equation X2 + Y2 = Z2. International journal of neutrosophic science, 22(2), 8–14. https://doi.org/10.54216/IJNS.220201
  7. [7] Galarza, F. C., Flores, M. L., Rivero, D. P., & Abobala, M. (2023). On weak fuzzy complex pythagoras quadruples. International journal of neutrosophic science, 22(2), 108–113. https://doi.org/10.54216/IJNS.220209
  8. [8] Abobala, M. (2024). On some novel results about weak fuzzy complex integers. Journal of neutrosophic and fuzzy systems, 8. https://doi.org/10.54216/JNFS.080202
  9. [9] Burden, R.L. & Faires, J. D. (2010). Numerical Analysis. Richard Stratton. https://colab.research.google.com/drive/1QDCMJhtmlUVmCumB6DarPiRJz-6uiwdh
  10. [10] Shihadeh, A., Salameh, W. M. M., Bataineh, M., Al-Tarawneh, H., Alahmade, A., & Al-Husban, A. (2024). On the geometry of weak fuzzy complex numbers and applications to the classification of some a-curves. International journal of neutrosophic science, 23(4), 369–375. https://doi.org/10.54216/IJNS.230428
  11. [11] Razouk, L., Mahmoud, S., & Ali, M. (2023). A computer program for the system of weak fuzzy complex numbers and their arithmetic operations using python. Galoitica: Journal of mathematical structures and applications, 8(1), 45–51. https://doi.org/10.54216/gjmsa.080104
  12. [12] Razouk, L., Mahmoud, S., & Ali, M. (2024). On the foundations of weak fuzzy complex-real functions. Journal of fuzzy extension and applications, 5(1), 116–140. https://doi.org/10.22105/jfea.2024.435955.1369
  13. [13] Edduweh, H., Heilat, A. S., Razouk, L., Khalil, S. A., Alsaraireh, A. A., & Al-Husban, A. (2025). On the weak fuzzy complex differential equations and some types of the 1st order 1st degree WFC-ODEs. International journal of neutrosophic science, 25(3), 450–468. https://doi.org/10.54216/IJNS.250338
  14. [14] Hatamleh, R. (2025). On a novel topological space based on partially ordered ring of weak fuzzy complex numbers and its relation with the partially ordered neutrosophic ring of real numbers. Neutrosophic Sets and Systems, 78, 577-590.. https://doi.org/10.5281/zenodo.14457896
  15. [15] Thomas Tomkins Warner. (2010). Numerical weather and climate prediction. Cambridge University Press. https://doi.org/10.1017/CBO9780511763243
  16. [16] Hull, J. C., & Basu, Sh. (1988). Options, futures, and other derivatives. Pearson India. https://books.google.nl/books/about/Options_Futures_and_other_Derivatives.html?id=CREwDwAAQBAJ&redir_esc=y
  17. [17] Khalil, H. K. (2002). Nonlinear systems. Prentice Hall. https://books.google.nl/books/about/Nonlinear_Systems.html?id=v_BjPQAACAAJ&redir_esc=y
  18. [18] Atkinson, K., Han, W., & Stewart, D. (2011). Numerical solution of ordinary differential equations. John Wiley & Sons, Inc. https://books.google.nl/books/about/Numerical_Solution_of_Ordinary_Different.html?id=SBvQ4ThK930C&redir_esc=y
  19. [19] Gander, W., Gander, M., & Kwok, F. (2010). Scientific Computing. Springer. https://books.google.nl/books/about/Scientific_Computing_An_Introduction_usi.html?id=QX7HBAAAQBAJ&redir_esc=y
  20. [20] Quarteroni, A., Sacco, R., and Saleri, F. (2006). Numerical mathematics. Springer. https://doi.org/10.1007/b98885
  21. [21] Cheney, W., Kincaid, D. (2008). Numerical mathematics and computing. Bob Pirtle. chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.hlevkin.com/hlevkin/60numalgs/Pascal/Numerical%20Mathematics%20and%20Computing.pdf

Published

2026-03-10

Issue

Vol. 3 No. 1 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Razouk, L. (2026). On the foundation of solving a first-order weak fuzzy complex initial value problem (WFC-IVP). Uncertainty Discourse and Applications, 3(1), 14-32. https://doi.org/10.48313/uda.vi.81

Similar Articles

1-10 of 51

You may also start an advanced similarity search for this article.