Fractional calculus, originating in the 17th century, deals with arbitrary-order integration and differentiation \cite{Fractional_derivative_BTE, math7050407}. Initially explored by mathematicians such as L’Hospital and Leibniz, it remained underdeveloped until recent decades, when applications in physics and engineering emerged. Fractional differential equations (FDEs) are now widely used to model complex phenomena, particularly in viscoelastic materials, with significant contributions from Bagley and Torvik \cite{Bagley_Torvik}. The most commonly used definitions are the Riemann-Liouville and Caputo derivatives, with the latter introduced to accommodate integer-order initial conditions. The primary objective of this talk is to approximate the fractional derivative of a given function using the univariate multinode Shepard method \cite{DellAccio:2018} through the Gauss-Jacobi quadrature formula. Subsequently, the proposed model is applied to the numerical solution of boundary value problems (BVPs) and initial value problems (IVPs), specifically addressing the Bagley-Torvik equations. Experimental results confirm the method's effectiveness, particularly in accurately approximating the Bagley-Torvik equation for both BVPs and IVPs. \begin{thebibliography}{99} \bibitem{Fractional_derivative_BTE} Rehman, M., Khan, M. A., A numerical method for solving boundary value problems for fractional differential equations. Applied Mathematical Modelling (2012)36: 894–907. https://doi.org/10.1016/j.apm.2011.07.045 \bibitem{math7050407} Garrappa, R., Kaslik, E., Popolizio, M., Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial. Mathematics (2019) 7. https://doi.org/10.3390/math7050407 \bibitem{Bagley_Torvik} Bagley, R.L., Torvik, P.J., Fractional calculus: a different approach to the analysis of viscoelastically damped structures, AIAA J. (1983) 21: 741–748. https://doi.org/10.2514/3.8142 \bibitem{DellAccio:2018} Dell’Accio, F., Di Tommaso, F., Hormann, K., Reconstruction of a function from Hermite-Birkhoff data. Applied Mathematics and Computation (2018) 318: 51–69. https://doi.org/10.1016/j.amc.2017.05.060 \end{thebibliography}