aspg-21-4188-1791468726 20261008141206 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 4 Alshaikh A. Shokeralla Department of Mathematics, Faculty of Science, Al-Baha University, Al-Aqiq 65931, Saudi Arabia 16.00 Normal false false false EN-US X-NONE AR-SA DefSemiHidden="false" DefQFormat="false" DefPriority="99" LatentStyleCount="371"> UnhideWhenUsed="true" QFormat="true" Name="heading 2"/> UnhideWhenUsed="true" QFormat="true" Name="heading 3"/> UnhideWhenUsed="true" QFormat="true" Name="heading 4"/> UnhideWhenUsed="true" QFormat="true" Name="heading 5"/> UnhideWhenUsed="true" QFormat="true" Name="heading 6"/> UnhideWhenUsed="true" QFormat="true" Name="heading 7"/> UnhideWhenUsed="true" QFormat="true" Name="heading 8"/> UnhideWhenUsed="true" QFormat="true" Name="heading 9"/> Name="index 1"/> Name="index 2"/> Name="index 3"/> Name="index 4"/> Name="index 5"/> Name="index 6"/> Name="index 7"/> Name="index 8"/> Name="index 9"/> UnhideWhenUsed="true" Name="toc 1"/> UnhideWhenUsed="true" Name="toc 2"/> UnhideWhenUsed="true" Name="toc 3"/> UnhideWhenUsed="true" Name="toc 4"/> 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Accent 6"/> Name="Grid Table 7 Colorful Accent 6"/> Name="List Table 1 Light Accent 1"/> Name="List Table 6 Colorful Accent 1"/> Name="List Table 7 Colorful Accent 1"/> Name="List Table 1 Light Accent 2"/> Name="List Table 6 Colorful Accent 2"/> Name="List Table 7 Colorful Accent 2"/> Name="List Table 1 Light Accent 3"/> Name="List Table 6 Colorful Accent 3"/> Name="List Table 7 Colorful Accent 3"/> Name="List Table 1 Light Accent 4"/> Name="List Table 6 Colorful Accent 4"/> Name="List Table 7 Colorful Accent 4"/> Name="List Table 1 Light Accent 5"/> Name="List Table 6 Colorful Accent 5"/> Name="List Table 7 Colorful Accent 5"/> Name="List Table 1 Light Accent 6"/> Name="List Table 6 Colorful Accent 6"/> Name="List Table 7 Colorful Accent 6"/> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:8.0pt; mso-para-margin-left:0in; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:Arial; mso-bidi-theme-font:minor-bidi; mso-font-kerning:1.0pt; mso-ligatures:standardcontextual;} This paper presents the Fractional Maxwell-Weibull Copula (FMWC) distribution to deal with the heavy tails, extended memory, and nonlinear dependence of price returns of Bitcoins, as the existing financial models face limitations in this aspect. The FMWC provides a flexible model that allows incorporating fractional Weibull distributions to capture persistent autocorrelation, Maxwell components to model significant price changes, and a Student-t copula to capture multivariate dependencies to discuss the volatile returns of Bitcoin. The FMWC was applied to historical Bitcoin data between January 2020 and May 2025 and showed better results than other models, such as Weibull, GARCH-t, and Maxwell-Log Logistic, with an MAE of 0.034374, RMSE of 0.0335, and log-likelihood of 4200.0. Its risk measures (VaR 95% = -0.07983, CVaR 95% = -0.10882) improve tail risk estimation, which is important in risk measurement and portfolio management. Robustness tests also validate its performance over periods and proper handling of outliers. Nevertheless, the FMWC is an excellent tool, despite its computational complexity issues, and can be used by investors, traders, and regulators. Further studies on the computational efficiencies and applications to other cryptocurrencies are required to increase their application in dynamic financial markets. 2025 309 326 4188 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260427 https://www.americaspg.com/journal/21/article/4188 https://www.americaspg.com/storage/71763649443.pdf