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Open Access Research Article

Fuzzy partial T-transforms applied to a system of PDE

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pp. 1099–1107Vol. 26Issue 6September 2023DOI: 10.47974/JIM-1609XML
Published Online:
08 Sep 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1609
Pages:
1099–1107

Abstract

Fuzzy partial integro-differential equations have widespread applications in the natural and applied sciences and engineering. The fuzzy T-transform transform is proposed as a new method for solving fuzzy partial differential equations in this research. Using very broad H-differentiability ideas, a formula for the first and second order fuzzy partial derivative has been derived. After an introduction to fuzzy partial T-transforms, fuzzy partial differential equations are developed. Finally, a working example has been presented to showcase the efficacy of the suggested approach.

Keywords

Subject Classifications

03Cxx03-XX03Exx

Acknowledgements

FRH-P909H66

References

[1] Abdul Rahman, N.A.; Ahmad, M.Z. Fuzzy Sumudu transform for solving fuzzy partial differential equations. J. Nonlinear Sci. Appl. 9(5), 3226-3239 (2016).
[2] Cano Y.C. Flores H. R. On new solutions of fuzzy differential Equations. Chaos, Solitons & Fract. 38(1): 112-119 (2008). https://doi.org/10.1016/j.chaos.2006.10.043.
[3] A. M. Wazwaz ‟Linear and non-linear  equation: method and application”, Springer, London (2011). 
[4] B. Bede, I. J. Rudas, nd A. L.Bencsik, ‟First Order Linear Fuzzy Differential Equations Under Generalized Differentiability,” Information Sciences, 177(7), 1648-1662 (2007). 
[5] C. Duraisamy , Usha B, ‟Another Approach to Solution of Fuzzy Differential Equations,” Applied Mathematical Sciences, 4(16): 777-790 (2010), 692; https://doi.org/10.3390/math8050692.
[6] Gündogdu, H. Ömer G.F, Solving nonlinear partial differential equations by using Adomian decomposition method modified decomposition method and Laplace decomposition method, Manas Journal of Engineering, 5(1), 1-13 (2017).
[7] Haydar A. K. Hassan R. H. Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n − 1 < b < n. Mathematical Problems in Engineering.  1-13 (2016). https://doi.org/10.1155/2016/6380978.
[8] Rodríguez-López R. Comparison results for fuzzy differential equations. Inform Sci. 178(6): 1756-1779 (2008). https://doi.org/10.1016/j.ins.2007.10.011.
[9] Salahshour, S. Allahviranloo T. Applications of fuzzy Laplace transforms, Soft Comput. 17(1), 145-158 (2013). https://doi.org/10.1007/s00500-012-0907-4.
[10] Seikkala S. On the fuzzy initial value problem, Fuzzy Sets and Systems. 24(3): 319-330 (1987). https://doi.org/10.1016/0165-0114(87)90030-3.
[11] Sleibi A. Alkiffai A.N, Solving Ordinary Differental Equations Using Fuzzy Transformation, Msc. these Kufa University, 2020.
[12] Ullah S. Farooq M. Ahmad L. Abdullah S. Application of fuzzy Laplace transforms for solving fuzzy partial Volterra integro-differential Equations, arXiv (2018). https://doi.org/10.48550/arXiv.1405.1895.
[13] Vignesh R. Thanga Rajeswari K. Venkatesh S. C. Natarajan, Alaeiyan M. On some degree-based irregularity indices of certain networks. Journal of Discrete Mathematical Sciences & Cryptography. 24(2), 617-628 (2021). https://doi.org/10.1080/09720529.2021.1892269.
[14] Vignesh R. Desikan K. Rajeswari K. T. Shanmugavelan S. Natarajan C. On certain degree-based irregularity indices of some nanotubes. Journal of Discrete Mathematical Sciences & Cryptography. 24(2), 603-615 (2021). https://doi.org/10.1080/09720529.2021.1891694.
[15] Wu H.-C. The improper fuzzy Riemann integral and its numerical integration, Inform. Sci. 111(1-4), 109-137 (1998). https://doi.org/10.1016/S0020-0255(98)00016-4.
[16] Wiley A. Sons, Applied Engineering Analysis, Tai-Ran Hsu, John (2018). 
[17] Zadeh L. A. Fuzzy sets, Inform, Cont. 8(3): 338-353 (1965). https://doi.org/10.1016/S0019-9958(65)90241-X.
[18] Zahid Z. Asif F. Jalil A. Khalaf M. & Farahani M.R. On leap indices of CNCk[n] by using line operator on its subdivision. Journal of Discrete Mathematical Sciences & Cryptography. 24(2), 343-352 (2021). https://doi.org/10.1080/09720529.2021.1882157.
[19] Zhang X. Ahmed F.S. Y. Li, L. Yan, Baig A.Q. Farahani M.R. A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique. Journal of Information and Optimization Sciences. 39(3), 673-694 (2018). https://doi.org/10.1080/02522667.2018.1443628.
[20] Zhang X. Razzaq A. Ali K. Rizvi S.T. R. Farahani M.R. A new approach to find eccentric indices of some graphs. Journal of Information and Optimization Sciences. 41(4), 2020, 865-877. https://doi.org/10.1080/02522667.2020.1744304.

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