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.
翻译:在本文中,引入了单埃登-佛勒分序方程式,并为其数字解决方案提出了一个计算方法。关于我们使用Boubaker多面体的解决方案的近似度,并定义了其分数衍生物操作矩阵的配方。然而,这一工具尚未使用,但这一区域尚未发现许多实际应用,这是第一次在此引入。卡普托分数衍生物工具的操作矩阵将这些问题转换成一个易计算解决方案的代数方程式系统。对数字示例进行了研究,以证明为寻找近似和精确解决方案而拟议方法的有效性和有效性。