In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some spectral collocation methods. Some illustrative examples are also given to show the validity and applicability of this method, and the obtained results are compared with the existing studies to highlight its high efficiency and neglectable error.

中文翻译：

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分数Bratu问题的Legendre谱方法

本文采用勒让德谱配点法（LSCM）求解分数阶布拉图方程。与其他数值方法相比，它显示了LSCM的高精度和低计算量。分数Bratu微分方程被转换为非线性系统，用于未知Legendre系数的代数方程，并使用某些频谱配位方法进行求解。通过举例说明该方法的有效性和适用性，并将所得结果与现有研究进行比较，以突出其高效性和可忽略的误差。