通过高斯积分逼近分数阶导数
Approximation of Fractional Derivatives Via Gauss Integration
AI总结：
本文利用修正高斯积分和高斯-拉盖尔积分逼近三类分数阶导数，通过处理拉普拉斯逆变换得到解，并建立误差界定理，数值例子验证了方法的有效性。
摘要：
本文考虑了使用修正高斯积分（MGI）和高斯-拉盖尔积分（GLI）对三类分数阶导数（FD）的逼近。这些分数阶导数的主要解依赖于拉普拉斯逆变换，而拉普拉斯逆变换通过上述方法处理。在修正积分形式中，权重和节点通过差分方程获得，从而为拉普拉斯逆变换及分数阶导数提供了合适的逼近形式。建立了定理以指示解的误差边界。给出了数值例子以阐明这些方法的应用结果。
英文摘要：
In this paper approximations of three classes of fractional derivatives (FD) using modified Gauss integration (MGI) and Gauss-Laguerre integration (GLI) are considered. The main solutions of these fractional derivatives depend on inverse of Laplace transforms, which are handled by these procedures. In the modified form of integration the weights and nodes are obtained by means of a difference equation, which gives a proper approximation form for the inverse of Laplace transform and hence the fractional derivatives. Theorem is established to indicate the boundary of the error of the solutions. Numerical examples are given to illuminate the results of the application of these methods.
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