In this article, we develop a new set of functions called fractional-order Alpert multiwavelet functions to obtain the numerical solution of fractional pantograph differential equations (FPDEs). The fractional derivative of Caputo type is considered. Here we construct the Riemann–Liouville fractional operational matrix of integration (Riemann–Liouville FOMI) using the fractional-order Alpert multiwavelet functions. The most important feature behind the scheme using this technique is that the pantograph equation reduces to a system of linear or nonlinear algebraic equations. We perform the error analysis for the proposed technique. Illustrative examples are examined to demonstrate the important features of the new method.

在本文中，我们开发了一组称为分数阶 Alpert 多小波函数的新函数，以获得分数阶受电弓微分方程 (FPDE) 的数值解。考虑了 Caputo 类型的分数导数。在这里，我们使用分数阶 Alpert 多小波函数构造积分的 Riemann-Liouville 分数运算矩阵 (Riemann-Liouville FOMI)。使用这种技术的方案背后最重要的特征是受电弓方程简化为线性或非线性代数方程组。我们对所提出的技术进行误差分析。检查说明性示例以证明新方法的重要特征。