In the current study, a numerical scheme for solving the nonlinear system of fractional Volterra integro‐differential equations via Legendre wavelet is proposed. The Legendre wavelet operational matrix of fractional integration is derived and utilized to alter the main system to a system of algebraic equations. In addition, the error estimate of the original system is investigated in detail. Lastly, several numerical examples are set forth to test the proposed method and the obtained numerical results are compared with those from the CAS wavelet method.

中文翻译：

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勒让德小波方法和误差估计对分数阶Volterra积分微分方程非线性系统的数值实现

在当前研究中，提出了一种通过勒让德小波求解分数阶Volterra积分微分方程非线性系统的数值方案。分数积分的勒让德小波运算矩阵被导出并用于将主系统更改为代数方程组。另外，详细研究了原始系统的误差估计。最后，列举了几个数值例子来验证该方法，并将所得数值结果与CAS小波方法的数值结果进行比较。