用于Caputo分数阶导数的单变量多节点Shepard方法：从逼近到Bagley-Torvik方程的求解
The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation
AI总结：
本文提出利用单变量多节点Shepard方法结合Gauss-Jacobi求积公式逼近Caputo分数阶导数，并应用于求解Bagley-Torvik方程的边值与初值问题，实验验证了其有效性。
摘要：
本文利用单变量多节点Shepard方法，通过Gauss-Jacobi求积公式逼近给定函数的分数阶导数。随后，将该方法应用于边值问题（BVPs）和初值问题（IVPs）的数值求解，特别是针对Bagley-Torvik方程。实验结果证实了该方法的有效性，特别是在精确逼近BVPs和IVPs的Bagley-Torvik方程方面。
英文摘要：
In this paper, we approximate the fractional derivative of a given function using the univariate multinode Shepard method through the Gauss-Jacobi quadrature formula. Subsequently, the proposed method 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
