This research propounds a fractional-order Legendre functions operational matrix of fractional integration in order to solve the fractional delay differential equations. The fractional derivative is regarded in the Caputo sense. The suggested method is implemented to reduce the problem to the solution of a system of algebraic equations. Using the presented method, some examples are solved and numerical stability of the proposed method is examined. Compared to other published methods, the presented technique proved to be more accurate.

中文翻译：

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解分数延迟微分方程的分数阶勒让德函数

提出了分数积分的分数阶勒让德函数运算矩阵，以求解分数延迟微分方程。分数导数在Caputo的意义上被视为。实施所建议的方法以将问题减少到代数方程组的解。使用提出的方法，解决了一些例子，并检验了该方法的数值稳定性。与其他已发布的方法相比，该技术被证明更加准确。