An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation

Liu Jianping; Li Xia; Wu Limeng

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An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation

机译：第二类Chebyshev多项式分数微分运算矩阵，用于求解多项变阶分数阶微分方程。

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The multiterm fractional differential equation has a wide application in engineering problems. Therefore, we propose a method to solve multiterm variable order fractional differential equation based on the second kind of Chebyshev Polynomial. The main idea of this method is that we derive a kind of operational matrix of variable order fractional derivative for the second kind of Chebyshev Polynomial. With the operational matrices, the equation is transformed into the products of several dependent matrices, which can also be viewed as an algebraic system by making use of the collocation points. By solving the algebraic system, the numerical solution of original equation is acquired. Numerical examples show that only a small number of the second kinds of Chebyshev Polynomials are needed to obtain a satisfactory result, which demonstrates the validity of this method.

机译：多项式分数阶微分方程在工程问题中具有广泛的应用。因此，我们提出了一种基于第二类切比雪夫多项式的多变量变分分数阶微分方程的求解方法。该方法的主要思想是为第二类Chebyshev多项式推导一种变阶分数阶导数的运算矩阵。通过运算矩阵，该方程式被转换为几个相关矩阵的乘积，也可以通过使用搭配点将其视为代数系统。通过求解代数系统，获得原始方程的数值解。数值算例表明，仅需少量的第二类Chebyshev多项式即可获得满意的结果，证明了该方法的有效性。

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来源
《Mathematical Problems in Engineering》 |2016年第6期|7126080.1-7126080.10|共10页
作者
Liu Jianping; Li Xia; Wu Limeng;
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Hebei Normal Univ Sci & Technol, Qinhuangdao 066004, Hebei, Peoples R China;

Hebei Normal Univ Sci & Technol, Qinhuangdao 066004, Hebei, Peoples R China;

Hebei Normal Univ Sci & Technol, Qinhuangdao 066004, Hebei, Peoples R China;

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6. Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix [O] . Jiaquan Xie, Qingxue Huang, Xia Yang -1

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7. An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials [O] . Jianping Liu, Xia Li, Limeng Wu 2016

机译：一种用于基于第二种Chebyshev多项式的可变阶分形差分方程的操作矩阵技术

An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation

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