This paper improves the modified multiwavelets bases of minimal search method for the fractional integro-differential equation. First, it shows the unique solvability of the equation. And then the Legendre multiwavelets are improved and the modified multiwavelets in reproducing kernel space are obtained. Subsequently, it is established a strict theory for obtaining the \(\varepsilon \)-approximate solution with minimal search method. Finally, some examples show that the modified continuous multiwavelets method is more effective and stable than the Legendre multiwavelets and other methods.

中文翻译：

---

一种基于修正Legendre多小波求解分数阶积分微分方程的极小搜索方法

本文对分数阶积分微分方程的最小搜索方法的改进多小波基进行了改进。首先，它显示了方程的唯一可解性。进而对Legendre多小波进行改进，得到在再生核空间中的修正多小波。随后，建立了用最小搜索方法获得\(\varepsilon\) -近似解的严格理论。最后，一些例子表明改进的连续多小波方法比Legendre多小波和其他方法更有效和稳定。