Block pulse functions are piecewise constant and not smooth enough. Therefore, they offer limited accuracy when used to approximate functions and unable to find highly accurate numerical solutions of fractional differential equations (FDEs). To overcome this problem, we present in this paper a new efficient numerical method for solving FDEs. A hybrid Bernoulli polynomials and block pulse functions operational matrix of fractional order integrals is derived and used to convert the underlying FDEs into a system of algebraic equations. The solutions of the FDEs are obtained by solving the algebraic equations. Simulation examples are given to verify the effectiveness of our proposed method, and the results show that the method is much more efficient and accurate than other known methods.

块脉冲功能是分段恒定的，不够平滑。因此，当用于逼近函数时，它们提供的精度有限，并且无法找到分数阶微分方程（FDE）的高精度数值解。为了克服这个问题，我们在本文中提出了一种求解FDE的新型有效数值方法。导出分数阶积分的混合伯努利多项式和块脉冲函数运算矩阵，并将其用于将基础FDE转换为代数方程组。FDE的解是通过求解代数方程获得的。仿真算例验证了所提方法的有效性，结果表明该方法比其他已知方法更有效，更准确。