In this paper, we have applied an iterative method to the singular and nonlinear fractional partial differential of Emden–Fowler equations types. Haar wavelets operational matrix of fractional integration will be used to solve the problem with the Picard technique. The singular equations turn to Sylvester equations that will be solved so that numerically solvable is very cost- effective. Moreover, the proposed technique is reliable enough to overcome the difficulty of the singular point at \(x = 0\). Numerical examples are providing to illustrate the efficiency and accuracy of the technique.

中文翻译：

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Haar小波配点法求解具有初始和边界条件的奇异和分数阶时间相关的Emden-Fowler方程

在本文中，我们对Emden-Fowler方程类型的奇异和非线性分数阶偏微分应用了迭代方法。分数积分的Haar小波运算矩阵将用于解决Picard技术的问题。奇异方程变为可求解的Sylvester方程，因此数值可解的成本效益非常高。而且，所提出的技术足够可靠以克服在\（x = 0 \）处的奇异点的困难。数值示例说明了该技术的效率和准确性。