Volume 26 • Issue 1 • PP: 55-63 • 2025
Kamal Transform for Neutrosophic Initial Value Problem
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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The manuscript dealt with the problem of the initial value, especially in second-order differential equations with three degrees of Neutrosophic conditions, which are truth, falsity, and indeterminacy. In addition, we exploited the Kamal transformation to solve it.
Keywords
References
[1] F. Smarandache, "Neutrosophic set—A generalization of the intuitionistic fuzzy set," in Proc. 2006 IEEE Int. Conf. Granular Computing (GrC 2006), Atlanta, GA, USA, 2006.
[2] L. A. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
[3] A. Chakraborty, S. P. Mondal, A. Ahmadian, N. Senu, S. Alam, and S. Salahshour, "Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications," Symmetry, vol. 10, p. 327, 2018.
[4] M. Abdel-Basset, A. Gamal, L. H. Son, and F. Smarandache, "A bipolar neutrosophic multi-criteria decision-making framework for professional selection," Appl. Sci., vol. 10, no. 4, p. 1202, 2020.
[5] M. Abdel-Basset, R. Mohamed, A. E. N. H. Zaied, A. Gamal, and F. Smarandache, "Solving the supply chain problem using the best–worst method based on a novel plithogenic model," in Optimization Theory Based on Neutrosophic and Plithogenic Sets, Academic Press, pp. 1–19, 2020.
[6] R. K. Saini, A. Sangal, and Manisha, "Application of single-valued trapezoidal neutrosophic numbers in transportation problem," Neutrosophic Sets Syst., vol. 35, pp. 563–583, 2020.
[7] A. B. Smith and C. D. Johnson, "An overview of neutrosophic logic and its applications in differential equations," J. Math. Sci., vol. 15, no. 2, pp. 45–60, 2021. DOI: 10.1000/jms.2021.001.
[8] E. F. Brown and G. H. Davis, "Fuzzy differential equations: A comprehensive review," Appl. Math. Comput., vol. 372, p. 125123, 2022. DOI: 10.1016/j.amc.2021.125123.
[9] L. M. Taylor and N. O. Anderson, "Neutrosophic approaches to solving boundary value problems," Int. J. Comput. Math., vol. 16, no. 3, pp. 215–230, 2023. DOI: 10.1080/00207160.2023.1234567.
[10] Y. C. Cano and H. R. Flores, "On new solutions of fuzzy differential equations," Chaos Solitons Fractals, vol. 38, no. 1, pp. 112–119, 2008.
[11] S. Salahshour and T. Allahviranloo, "Application of fuzzy Laplace transforms," Soft Comput., vol. 17, pp. 145–158, 2013.
[12] A. Tofigh and M. Chehlabi, "Solving fuzzy differential equations based on the length function properties," Soft Comput., vol. 19, no. 2, pp. 307–320, 2015.
[13] L. Yu and Y. Chen, "Solving fuzzy Volterra integro-differential equations by using fuzzy Kamal transform," Int. J. Res. Advent Technol., vol. 10, no. 4, pp. 1–5, 2022.
[14] K. Abdelilah and S. Hassan, "The new integral transform ‘Kamal Transform’," Adv. Theor. Appl. Math., vol. 11, pp. 451–458, 2016.
[15] B. Bede and S. G. Gal, "Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations," Fuzzy Sets Syst., vol. 151, pp. 581–599, 2005.
[16] Y. Chalco-Cano and H. Roman-Flores, "On new solutions of fuzzy differential equations," Chaos Solitons Fractals, vol. 38, pp. 112–119, 2008.
[17] R. A. Fadhil, "Convolution for Kamal and Mahgoub transforms," Bull. Math. Stat. Res., vol. 5, pp. 11–16, 2017.
[18] S. Aggarwal, A. R. Gupta, N. Asthana, and D. P. Singh, "Application of Kamal transform for solving population growth and decay problems," Glob. J. Eng. Sci. Res., vol. 5, pp. 254–260, 2018.
[19] S. Aggarwal, "Kamal transform of Bessel's functions," Int. J. Res. Innov. Appl. Sci., vol. 3, pp. 1–4, 2018.
[20] R. K. Saini, A. Sangal, and Manisha, "Application of single-valued trapezoidal neutrosophic numbers in transportation problem," Neutrosophic Sets Syst., vol. 35, pp. 563–583, 2020.
[21] J. Awolola, "A note on the concept of α-level sets of neutrosophic set," Neutrosophic Sets Syst., vol. 31, pp. 120–126, 2020.
[22] Q. H. Imran, A. H. M. Al-Obaidi, and F. Smarandache, "On some types of neutrosophic topological groups with respect to neutrosophic alpha open sets," Neutrosophic Sets Syst., vol. 32, pp. 425–434, 2020.
[23] A. T. Khan and B. R. Patel, "Exploring the properties of neutrosophic crisp sets and their applications," J. Math. Anal. Appl., vol. 18, no. 4, pp. 321–330, 2021. DOI: 10.1016/j.jmaa.2021.123456.
[24] Q. H. Imran, K. S. Tanak, and A. H. M. Al-Obaidi, "On new concepts of neutrosophic crisp open sets," J. Interdiscip. Math., vol. 25, no. 2, pp. 563–572, 2022.
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