A new technique based on beta functions is applied to compute the exact formula for the Riemann–Liouville fractional integral of the fractional-order generalized Chelyshkov wavelets. An approximation method based on the wavelets is proposed to effectively solve nonlinear fractional differential equations. Illustrative examples show that the proposed method gives solutions with less errors in comparison with the previous methods.

中文翻译：

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求解非线性分数阶微分方程的一种有效方法

应用一种基于 beta 函数的新技术来计算分数阶广义 Chelyshkov 小波的 Riemann-Liouville 分数积分的精确公式。提出了一种基于小波的近似方法来有效求解非线性分数阶微分方程。说明性示例表明，与以前的方法相比，所提出的方法提供的解决方案具有更少的错误。