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Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel
Advances in Difference Equations ( IF 4.1 ) Pub Date : 2021-03-25 , DOI: 10.1186/s13662-021-03349-1
M. H. Heydari , Z. Avazzadeh , A. Atangana

In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative with non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and a computational method is proposed for its numerical solution. The desired method is established upon the shifted Jacobi polynomials and their operational matrix of variable-order fractional differentiation (which is extracted in the present study) together with the spectral collocation method. The presented method transforms obtaining the solution of the main problem into obtaining the solution of an algebraic system of equations. Several numerical examples are examined to show the validity and the high accuracy of the established method.



中文翻译:

非线性奇异变量阶时间分数阶Emden-Fowler方程的位移Jacobi多项式,该方程由非奇异核导数生成

在这项工作中,引入了非线性奇异变量阶分数阶Emden-Fowler方程,该方程涉及具有非奇异核的导数(在Atangana–Baleanu–Caputo类型中),并为其数值解提出了一种计算方法。期望的方法是基于移位的Jacobi多项式及其变阶分数阶微分的运算矩阵(在本研究中提取的)以及频谱搭配方法。提出的方法将获得主要问题的解转化为获得代数方程组的解。通过数值算例验证了所建立方法的正确性和准确性。

更新日期:2021-03-25
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