Volume 27 • Issue 1 • PP: 272-277 • 2026
A Developed Non-Polynomial Spline Method for Solving Fuzzy Partial Differential Equations
Abstract
This research introduces a novel approach to the non-polynomial spline dependent method for solving fuzzy partial differential equations. The tensor product of non-polynomial spline functions is derived in order to obtaining a solution to fuzzy partial differential equations, such as fuzzy hyperbolic and parabolic equations. The advantage of this method is that it simplifies the complex procedure that arises from the term of the typical product of a fuzzy number by fuzzy functions. Examples are presented to show that the outcomes of the research indicate that the technique is extremely useful to construct the solution to the desired fuzzy partial differential equations.
Keywords
References
[1] Bakheet, E. A. Z. Alnussairy, Ismail, and N. Amin, "Generalized power-law model of magnetohydrodynamic blood flow with heat transfer," Indian J. Public Health Res. Dev., vol. 9, no. 12, pp. 794-800, 2018.
[2] L. A. Zadeh, "Fuzzy Sets," Inf. Control, vol. 8, pp. 338-353, 1965.
[3] J. Smith, A. Johnson, and R. Lee, "A Comprehensive Survey on Machine Learning Techniques for IoT Security," Journal of Computer Networks and Communications, vol. 2022, no. 5, pp. 1-15, 2022.
[4] S. S. Chang and L. A. Zadeh, "On fuzzy mapping and concept fuzzy sets," in Fuzzy Logic and Fuzzy Systems, World Scientific, 1996.
[5] D. Dubois and H. Prade, "Towards fuzzy differential calculus part 3: Differentiation," Fuzzy Sets Syst., vol. 8, no. 3, pp. 225-233, 1982.
[6] M. L. Puri and D. A. Ralescu, "Differentials of fuzzy functions," J. Math. Anal. Appl., vol. 91, no. 2, pp. 552-558, 1983.
[7] R. Goetsehel Jr. and W. Voxmax, "Elementary fuzzy calculus," Fuzzy Sets Syst., vol. 18, no. 1, pp. 31-43, 1986.
[8] Khan and T. Aziz, "Parametric cubic spline approach to the solution of a system of second order boundary value problems," J. Optim. Theory Appl., vol. 118, no. 1, pp. 45-54, 2003.
[9] Q. Ding and P. J. Wong, "Mid-knot cubic non-polynomial spline for a system of second-order boundary value problems," Bound. Value Probl., vol. 2018, no. 1, p. 156, 2018.
[10] N. N. Hasan, "Cubic non-polynomial spline approach to the solution of Lane-Emden equations," IJICIC, vol. 17, no. 5, pp. 1681-1689, 2021.
[11] N. N. Hasan, "Non-polynomial spline functions for solving two-dimensional linear fuzzy Fredholm integral equations," ICIC-ELB, vol. 13, no. 7, pp. 673-679, 2022.
[12] Z. A. Ibrahim and N. N. Hasan, "Approximation solution of fuzzy Volterra integral equation," ICIC-ELB, vol. 13, no. 9, pp. 907-913, 2022.
[13] O. Kaleva, "Fuzzy differential equations," Fuzzy Sets Syst., vol. 24, no. 3, pp. 301-317, 1987.
[14] Z. Gong and Y. Hoa, "Fuzzy Laplace transforms and systems based on the Henstock integral and its applications in discontinuous fuzzy systems," Fuzzy Sets Syst., vol. 283, no. C, pp. 1-28, 2019.
[15] T. Allahvikanloo and Z. Gouyandeha, "On fuzzy solution for heat equation based on generalized Fukuhara differentiability," Fuzzy Sets Syst., vol. 265, pp. 1-23, 2015.
[16] D. S. G. Pollock, "On Kronecker products, tensor products and matrix differential calculus," Int. J. Comput. Math., vol. 90, no. 11, pp. 2462-2476, 2013.
Cite This Article
Choose your preferred format