Abstract In this work, we introduce a useful and efficient calculation method for solving linear fractional pantograph delay equations (FPDEs). The proposed method is primarily dependent on the least-squares approximation technique. After embedding the problem into a minimization problem, it solves the Lagrange multiplier method. The convergence analysis is theoretically proved. Finally, some numerical examples singled out to show the usefulness and capability of the suggested approach.

中文翻译：

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用一种有效的计算方法求解分数阶受电弓延迟方程

摘要 在这项工作中，我们介绍了一种有用且有效的计算方法来求解线性分数缩放延迟方程 (FPDE)。所提出的方法主要依赖于最小二乘逼近技术。将问题嵌入到最小化问题后，求解拉格朗日乘子法。理论上证明了收敛性分析。最后，一些数值例子被挑出来展示了所建议方法的有用性和能力。