We give an effective method for solving fractional Riccati differential equations. We first define the fractional-order Boubaker wavelets (FOBW). Using the hypergeometric functions, we determine the exact values for the Riemann-Liouville fractional integral operator of the FOBW. The properties of FOBW, the exact formula, and the collocation method are used to transform the problem of solving fractional Riccati differential equations to the solution of a set of algebraic equations. These equations are solved via Newton's iterative method. The error estimation for the present method is also determined. The performance of the developed numerical schemes is assessed through several examples. This method yields very accurate results. The given numerical examples support this claim.

给出了求解分数阶Riccati微分方程的一种有效方法。我们首先定义分数阶 Boubaker 小波 (FOBW)。使用超几何函数，我们确定 FOBW 的 Riemann-Liouville 分数积分算子的精确值。利用FOBW的性质、精确公式和搭配方法，将求解分数阶Riccati微分方程的问题转化为一组代数方程的解。这些方程通过牛顿迭代法求解。还确定了本方法的误差估计。通过几个例子来评估所开发的数值方案的性能。这种方法产生非常准确的结果。给定的数值例子支持这一主张。