aspg-21-2716-1791475393 20261008160313 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 2 Mohamed Nedal Khatib Faculty of Science, Department of Mathematics, Idlib University, Idlib, Syria Ahmed Hatip Department of Mathematics, University of Gaziantep, Turkey 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. 2024 08 18 2716 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240201 https://www.americaspg.com/journal/21/article/2716 https://www.americaspg.com/storage/41715239544.pdf