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针对一类非线性分数阶微分方程,采用 Legendre 小波法对非线性分数阶微分方程进行研究.结合 Block Pulse 函数给出 Legendre 小波的分数阶积分算子矩阵,利用 Block Pulse 函数的定义与 Legendre 小波积分算子矩阵的性质将非线性分数阶微分方程转换为非线性代数方程组,进而对其数值解和误差分析进行研究.结果表明:随着点数增多,数值解的精确度增加.数值算例验证了小波法的可行性和有效性.“,”In order to obtain a numerical solution for nonlinear differential equations of fractional order,this study obtains Legendre wavelet through Legendre polynomial. Subsequently, it derives the integral operational matrix of fractional order of Legendre wavelet through block pulse functions. Furthermore, the nonlinear differential equations are transformed into a nonlinear system of algebraic equations using the properties of block pulse functions and the integral operational matrix of fractional order of Legendre wavelet. Therefore, the numerical solution of original equations can be obtained. The numerical example demonstrates the effectiveness and feasibility of the method proposed.