Volume 24 , Issue 2 , PP: 08-18, 2024 | Cite this article as | XML | Html | PDF
Mohamed Nedal Khatib 1 * , Ahmed Hatip 2
Doi: https://doi.org/10.54216/IJNS.240201
Depending on the geometric isometry (AH-Isometry), it has been proven that every Neutrosophic real function is equivalent to three real functions. Then, the foundation of the Refined Netrusophic calculus was established, where new definitions of Refined Netrusophic integration and Refined Netrusophic differentiation were introduced, along with some illustrative examples. Following that, definitions for the Refined Netrusophic gamma function and Refined Netrusophic beta function were presented to pave the way towards achieving the desired goal, which is Refined Netrusophic Fractional calculus.
Refined Neutrosophic real function , Refined Neutrosophic Integration , Refined Neutrosophic Derivative , Refined Netrusophic Fractional integral and Refined Netrusophic Fractional Derivative.
[1] Abobala, M., "AH-Subspaces in Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 6 , pp. 80-86. 2020.
[2] Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.
[3] Sankari, H., and Abobala, M., "Neutrosophic Linear Diophantine Equations With two Variables", Neutrosophic Sets and Systems, Vol. 38, pp. 22-30, 2020.
[4] Sankari, H., and Abobala, M." n-Refined Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 36, pp. 1-11. 2020.
[5] Alhamido, R., and Abobala, M., "AH-Substructures in Neutrosophic Modules", International Journal of Neutrosophic Science, Vol. 7, pp. 79-86 . 2020.
[6] Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability", American Research Press. Rehoboth, 2003.
[7] Suresh, R., and S. Palaniammal,. "Neutrosophic Weakly Generalized open and Closed Sets", Neutrosophic Sets and Systems, Vol. 33, pp. 67-77,. 2020.
[8] Olgun, N., and Hatip, A., "The Effect Of The Neutrosophic Logic On The Decision Making, in Quadruple Neutrosophic Theory And Applications", Belgium, EU, Pons Editions Brussels,pp. 238-253. 2020.
[9] Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal of Neutrosophic Science", Vol. 0, pp. 67-76 . 2019.
[10] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0, pp. 27-34. 2020.
[11] Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 7, pp. 74-78. 2020.
[12] Smarandache, F., and Abobala, M., n-Refined neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 , pp. 83-90, 2020.
[13] Abobala, M., On Some Special Substructures of Neutrosophic Rings and Their Properties, International Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.
[14] Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of Neutrosophic Science, Vol. 5, pp. 59-66. 2020.
[15] Sankari, H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.
[16] K. Miller, B. Ross; An Introduction to the F ractional Calculus and F ractional Differential Equations, John Wiley & Sons, Inc., 1993.
[17] A. A. A. Agboola, "On Refined Neutrosophic Algebraic Structures," Neutrosophic Sets and Systems, pp. 99-101, 2015.
[18] Mehmet Celik, Ahmed Hatip, "On the Refined AH-Isometry and Its Applications in RefinedNeutrosophic Surfaces," Galoitica Journal Of Mathematical Structures And Applications (GJMSA), vol. 02, no. 01, pp. 21-28, July 2022.
[19] F. Smarandache, "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets," Inter. J. Pure Appl. Math., pp. 287-297, 2005.
[20] M. Ali, F. Smarandache, M. Shabir and L. Vladareanu, "Generalization of Neutrosophic Rings and Neutrosophic Fields," Neutrosophic Sets and Systems, vol. 5, pp. 9-14, 2014.
[21] F. Smarandache, Introduction to Neutrosophic Statistics, USA: Sitech & Education Publishing, 2014.
