求解某些分数阶微分方程的移位单原子超球面逼近
Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations
摘要：
本文的目的是显示和解释一个新的公式，表示与最终的衍生物的移位Monic超非球面多项式（SMUPs）的任何次数和任何分数阶使用移位Monic超非球面多项式本身。我们还创建了一个直接法解决的线性或非线性多阶分数阶微分方程（FDES）的常系数涉及谱Galerkin方法。空间近似及其分数阶导数（在Caputo意义上描述）是使用移位的Monic Ultraspherical多项式建立的。
英文摘要：
The purpose of this paper is to show and explain a new formula that indicates with finality the derivatives of Shifted Monic Ultraspherical polynomials (SMUPs) of any degree and for any fractional-order using the shifted Monic Ultraspherical polynomials themselves. We also create a direct method solution for the linear or nonlinear multi-order fractional differential equations (FDEs) with constant coefficients involving a spectral Galerkin method. The spatial approximation with its fractional order derivatives (described in the Caputo sense) are built using shifted Monic Ultraspherical polynomials.
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