Legendre wavelets and their exact Riemann-Liouville fractional integrals are used to compute numerical solutions to fractional delay differential equations, by reducing the problem to algebraic equations. An error bound of Legendre wavelet approximation is analytically computed, which implies the approximation converges when the degree of the Legendre polynomials or the number of wavelets approaches infinity. Finally, several numerical examples are considered.

中文翻译：

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分数延迟微分方程的勒让德小波方法

Legendre 小波及其精确的 Riemann-Liouville 分数阶积分用于通过将问题简化为代数方程来计算分数阶延迟微分方程的数值解。分析计算勒让德小波逼近的误差界，这意味着当勒让德多项式的次数或小波数接近无穷大时逼近收敛。最后，考虑了几个数值例子。