Volume 27 • Issue 2 • PP: 320-340 • 2026
Solution of Intuitionistic Fuzzy System of Linear Volterra Integro-differential Equations by a Novel Hybrid Method
View PDF Abstract
Our study addresses the intuitionistic fuzzy system of linear Volterra-integro-differential equations of the second kind. Intuitionistic fuzzy General Transform (I-F-G-transform) method has been used to find the exact solution of these systems. We present two numerical examples for illustrating the applicability of the Intuitionistic fuzzy General integral transform method.
Keywords
References
[1] K. S. Aboodh. (2013). The New Integral Transform Aboodh Transform, Global Journal of pure and Applied Mathematics, 9(1), 35-43.
[2] S. A. P. Ahmadi, H. Hosseinzadeh, A. Y. Cherati. (2019). A New Integral Transform for Solving Higher Order Linear Ordinary Differential Equations, Nonlinear Dyn Syst Theory, 19(2), 243-52.
[3] K.T. Atanassov. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20, 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3.
[4] B. Bede, I. J. Rudas, A. L. Bencsik. (2007). First order linear fuzzy differential equations under generalized di6erentiability, Information Sciences, 177( 7), 1648-1662. https://doi.org/10.1016/j.ins.2006.08.021
[5] S. S. L. Chang, L. Zadeh. (1972). On fuzzy mapping and control, IEEE Trans. Systems Man Cybernet, 2, 30-34. https://doi.org/10.1109/TSMC.1972.5408553
[6] H. Eltayeb, A. Kiliman, and B. Fisher. (2010). A new integral transform and associated distributions, Integral Transforms Special Funct. 21(5), 367-379.
[7] T. M. Elzaki. (2011). The new integral transform Elzaki Transform. Global Journal of Pure and Applied Mathematics, 7(1), 57-64.
[8] R. Ettoussi, S. Melliani, M. Elomari and L. S. Chadli. (2015). Solution of Intuitionistic Fuzzy Differential Equations by successive approximation method, Notes on Intuitionistic Fuzzy Sets, 21(2), 51-62.
[9] P. Grzegorzewski. (2003). The hamming distance between intuitionistic fuzzy sets, Proceedings of the 10th IFSA World Congress, Istanbul, Turkey, 35-38.
[10] H. Jafari. (2021). A new general integral transform for solving integral equations, Journal of Advanced Research, 32, 133-138. https://doi.org/10.1016/j.jare.2020.08.016
[11] H. Kamal. (2016). A. Sedeeg, The new integral transform Kamal transform. Adv Theoret Appl Mathe, 11(4), 451-8.
[12] M. Matloka. (1987). On fuzzy integrals, 2nd Polish Symp.on Interval. Politechnika Poznansk, 167-170.
[13] M. Mohand, A. Mahgoub. (2017). The new integral transform Mohand transfrom, Adv. Theor. Appl. Math, 12(2), 113–120.
[14] M. Mohand, M. Abdelrahim. (2019). The new integral transform Sawi Transform, Adv Theoretical Appl Math, 14(1), 81–87.
[15] S. Melliani, M. Elomari, L. S. Chadli and R. Ettoussi. (2015). Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy Sets, 21(1), 43-53.
[16] V. Nirmala, V. Parimala, P. Rajarajeswari. (2015). Modified Euler Method for Finding Numerical Solution of Intuitionistic Fuzzy Differential Equation under Generalised Differentiability Concept, International Journal of Applied Engineering Research, 10(72), 40-45.
[17] J.Y. Park, Y.C. Kwan, J.V. Jeong. (1995). Existence of solutions of fuzzy integral equations in Banach spaces, Fuzzy Sets and System, 72 (3), 373-378. https://doi.org/10.1016/0165- 0114(94)00296-J
[18] K. Shah , M. Junaid , N. Ali. (2015). Extraction of laplace, sumudu, fourier and mellin transform from the natural transform. Journal of Applied Environmental and Biological Sciences, 5(9), 108-115.
[19] L.A. Zadeh. (1965). Fuzzy sets, Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019- 9958(65)90241-X.
Cite This Article
Choose your preferred format