International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 25 , Issue 3 , PP: 258-264, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment

Azal J. Mera 1 * , Huda A. Hadi 2 , Sahar M. Jabbar 3

  • 1 Department of Mathematics, College of Education for Pure Science, University of Babylon, Babil, Iraq - (azal.mera@uobabylon.edu.iq)
  • 2 Department of Mathematics, College of Education for Pure Science, University of Babylon, Babil, Iraq - (hudahdi@uobabylon.edu.iq)
  • 3 Department of Mathematics, College of Education for Pure Science, University of Babylon, Babil, Iraq - (pure.saher.mohsen@uobabylon.edu.iq)
  • Doi: https://doi.org/10.54216/IJNS.250323

    Received: March 07, 2024 Revised: June 02, 2024 Accepted: October 17, 2024
    Abstract

    This manuscript presents a novel approach for solving first-order initial value problems by leveraging the Fuzzy Kamal Transform within a Neutrosophic framework. By integrating fuzzy logic with Neutrosophic set theory, the method adeptly addresses uncertainties inherent in differential equations. The efficacy of this method is demonstrated through the exposition of various illustrative examples.

    Keywords :

    Fuzzy transform , Neutrosophic logic , Kamal transform , Fuzzy Kamal transform

    References

    [1] Zadeh, L.A.(1965)"Fuzzy sets", Information and Control ,Vol.8,No.3,pp.338-353.

    [2] Atanassov, K.T.(1986)"Intuitionistic fuzzy sets", Fuzzy Sets and Systems,Vol.20,No.1,pp.87-96.

    [3] Ejegwa, P.A.; Akowe, S.O.;Otene,P.M.;Ikyule,J.M.(2014)"An Overview on intuitionistic Fuzzy sets ,Int. J. of Scientific and Technology Research ,Vol.3,No.3,pp.142-144.

    [4] Smarandache, F.(2006)"Neutrosophic set-A generalization of the intuitionistic Fuzzy set", Conference:2006 IEEE Int.Con. On Granular Computing, GrC, 2006, Atlanta,Georgia,USA.

    [5] Wang,H.;Smarandache,F.;Zhang,Y.Q.;Sunderraman,R.(2010) "Single Valued Neutrosophic sets", Multispace a Multistructure,Vol.4,pp.410- 413.

    [6] Chakraborty,A.;Mondal,S.P.;Ahmadian,A.;Senu,N.;Alam,S.; Salahshour ,S.(2018) "Different forms of triangular Neutrosophic numbers,de-Neutrosophication techniques,And their applications",Symmetry,Vol.10,pp.327.

    [7] Jabbar, S.M., Alkiffai, A.N., Mera, A.( 2023)" Solving Thermal System Problem Via Fuzzy Mohand Transform Under Neutrosophic Initial Conditions", Int. j. of Neutrosophic Science 21(1), pp. 8–13

    [8] Jabbar, S.M., Alkiffai, A.N., Mera, A.( 2024)" Fuzzy Logic Used to Solve ODEs of Second Order Under Neutrosophic Initial Conditions", Int. j. of Neutrosophic Science 2024, 23(1), pp. 51–58

    [9] Le Yu, Yumei Chen. (2022). Solving Fuzzy Volterra Integro-Differential Equations By Using Fuzzy Kamal Transform. International Journal of Research in Advent Technology, 10(4), 1-5.

    [10] D. Dubois, H. Prade, (1982) “Towards fuzzy differential calculus part 1: Integration of fuzzy mappings”. Fuzzy Sets and Systems, vol. 8, pp. 1-17.

    [11] D. Dubois, H. Prade, (1982) “Towards fuzzy differential calculus part 2: Integration on fuzzy intervals”. Fuzzy Sets and Systems. vol. 8, pp. 105-116.

    [12] D. Dubois, H. Prade.( 1982) “Towards fuzzy differential calculus part 3: Differentiation”. Fuzzy Sets and Systems. vol. 8, pp. 225-233.

    [13] M.L. Puri, D.A. Ralescu.( 1983) “Differentials of fuzzy functions”. Journal of Mathematical Analysis and Applications. vol. 91, pp. 552-558.

    [14] J.J. Buckley, T. Feuring.( 2000) “Fuzzy differential equations”. Fuzzy Sets Systems. vol. 110, pp. 43-54.

    [15] R. Goetschel, W. Voxman,( 1986) “Elementary fuzzy calculus”. Fuzzy Sets Systems. vol. 18, pp. 31-43.

    [16] K. Abdelilah, S. Hassan,( 2016) “The new integral transform ``Kamal Transform''”. Advances in Theoretical and Applied Mathematics, vol. 11, pp. 451-458.

    [17] B. Bede, S.G. Gal,( 2005) “Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations”. Fuzzy Sets and Systems, vol. 151, pp.581-599.

    [18] Y. Chalco-Cano, H. Roman-Flores, (2008) “On new solutions of fuzzy differential equations”. Chaos, Solitons Fractals, vol. 38, pp.112-119.

    [19] R.A. Fadhil.( 2017) “Convolution for Kamal and Mahgoub transforms”. Bulletin of Mathematics and Statistics Research, vol. 5, pp.11-16.

    [20] S. Aggarwal, A.R. Gupta, N. Asthana, D.P. Singh,( 2018) “Application of Kamal transform for solving population growth and decay problems”. Global Journal of Engineering Science and Researches, vol. 5, pp.254-260.

    [21] S. Aggarwal,( 2018) “Kamal transform of Bessel's functions”. International Journal of Research and Innovation in Applied Science, vol. 3, pp.1-4.

    [22] Saini,R.K.;Sangal,A.;Manisha(2020)"Application of single valued Trapezoidal Neutrosophic numbers in transportation problem",Neutrosophic Sets and Systems",Vol.35,pp.563-583.

    [23] Awolola,J.(2020)"A Note on the concept of α-level sets of Neutrosophic set", Neutrosophic Sets and Systems,Vol.31,pp.120-126.

    [24] Q. H. Imran, A. H. M. Al-Obaidi, & Smarandache, F., On Some Types of Neutrosophic Topological Groups with Respect to Neutrosophic Alpha Open Sets. Neutrosophic Sets and Systems, 32, (2020), 425-434.

    [25] Q. H. Imran, R. K. Al-Hamido and A. H. M. Al-Obaidi, on new types of weakly neutrosophic crisp continuity. Neutrosophic Sets and Systems, 38(2020), 179-187.

    [26] Q. H. Imran, K. S. Tanak and A. H. M. Al-Obaidi, on new concepts of neutrosophic crisp open sets. Journal of Interdisciplinary Mathematics, 25(2)(2022), 563-572.

     

     

    Cite This Article As :
    J., Azal. , A., Huda. , M., Sahar. Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 258-264. DOI: https://doi.org/10.54216/IJNS.250323
    J., A. A., H. M., S. (2025). Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment. International Journal of Neutrosophic Science, (), 258-264. DOI: https://doi.org/10.54216/IJNS.250323
    J., Azal. A., Huda. M., Sahar. Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment. International Journal of Neutrosophic Science , no. (2025): 258-264. DOI: https://doi.org/10.54216/IJNS.250323
    J., A. , A., H. , M., S. (2025) . Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment. International Journal of Neutrosophic Science , () , 258-264 . DOI: https://doi.org/10.54216/IJNS.250323
    J. A. , A. H. , M. S. [2025]. Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment. International Journal of Neutrosophic Science. (): 258-264. DOI: https://doi.org/10.54216/IJNS.250323
    J., A. A., H. M., S. "Solving of First Order Initial Value Problem Using Fuzzy Kamal Transform in Neutrosophic Environment," International Journal of Neutrosophic Science, vol. , no. , pp. 258-264, 2025. DOI: https://doi.org/10.54216/IJNS.250323