求解分数阶Emden-Fowler问题的一个新的基于Boubaker多项式的运算矩阵
A new operational matrix based on Boubaker polynomials for solving fractional Emden-Fowler problem
摘要：
本文介绍了分数阶奇异Emden-Fowler方程，并给出了其数值解的计算方法。对于近似的解决方案，我们已经使用Boubaker多项式，并定义其分数阶导数运算矩阵的制定。这个工具还没有被使用，然而，这一领域还没有找到很多实际应用，这里是第一次介绍。Caputo分数导数工具的运算矩阵将这些问题转换为一组代数方程，其解简单且易于计算。数值算例验证了该方法的有效性，并证明了该方法的有效性。
英文摘要：
In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the formulation for its fractional derivative operational matrix. This tool was not used yet, however, this area has not found many practical applications yet, and here introduced for the first time. The operational matrix of the Caputo fractional derivative tool converts these problems to a system of algebraic equations whose solutions are simple and easy to compute. Numerical examples are examined to prove the validity and the effectiveness of the proposed method to find approximate and precise solutions.
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