Kamal Transform for Neutrosophic Initial Value Problem

Azal J.; Huda A.; Sahar M.

doi:https://doi.org/10.54216/IJNS.260105

Full Length Article

Volume 26 • Issue 1 • PP: 55-63 • 2025

Kamal Transform for Neutrosophic Initial Value Problem

Azal J. Mera ^1*

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,

Huda A. Hadi ¹

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,

Sahar M. Jabbar ¹

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¹Department of Mathematics, College of Education for Pure Science, University of Babylon, Babil, Iraq

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.260105

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Received: October 13, 2024 Revised: January 02, 2025 Accepted: January 29, 2025

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Abstract

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

Fuzzy logic Neutrosophic logic Kamal transform Neutrosophic initial conditions

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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Mera, Azal J., Hadi, Huda A., Jabbar, Sahar M.. "Kamal Transform for Neutrosophic Initial Value Problem." International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 1, 2025, pp. 55-63. DOI: https://doi.org/10.54216/IJNS.260105

Mera, A., Hadi, H., Jabbar, S. (2025). Kamal Transform for Neutrosophic Initial Value Problem. International Journal of Neutrosophic Science, Volume 26(Issue 1), 55-63. DOI: https://doi.org/10.54216/IJNS.260105

Mera, Azal J., Hadi, Huda A., Jabbar, Sahar M.. "Kamal Transform for Neutrosophic Initial Value Problem." International Journal of Neutrosophic Science Volume 26, no. Issue 1 (2025): 55-63. DOI: https://doi.org/10.54216/IJNS.260105

Mera, A., Hadi, H., Jabbar, S. (2025) 'Kamal Transform for Neutrosophic Initial Value Problem', International Journal of Neutrosophic Science, Volume 26(Issue 1), pp. 55-63. DOI: https://doi.org/10.54216/IJNS.260105

Mera A, Hadi H, Jabbar S. Kamal Transform for Neutrosophic Initial Value Problem. International Journal of Neutrosophic Science. 2025;Volume 26(Issue 1):55-63. DOI: https://doi.org/10.54216/IJNS.260105

A. Mera, H. Hadi, S. Jabbar, "Kamal Transform for Neutrosophic Initial Value Problem," International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 1, pp. 55-63, 2025. DOI: https://doi.org/10.54216/IJNS.260105

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