本文以神经网络理论为基础,提出了基于余弦基神经网络的分数阶微分初值问题计算算法。余弦基神经网络算法取代了初值问题的解析解,由此而得到分数阶微分方程的数值解。分数阶微分方程(FDE)作为经典的整数阶微分方程的推广,它是将整数阶的导数用分数阶的导数来代替。与传统的整数阶微分方程相比较,由于分数阶导数是一个拟微分算子,具有良好的记忆性和遗传性,以及明显的非局部性,因此分数阶微积分方程能更好的模拟自然界中的一些物理过程和 Based on the theory of neural network, this paper proposes a new method to calculate the fractional differential initial value problem based on the cosine basis neural network. The cosine basis neural network algorithm replaces the analytic solution of the initial value problem, and the numerical solution of the fractional differential equation is obtained. As a generalization of classical integral differential equations, fractional differential equations (FDEs) replace fractional derivatives with fractional derivatives. Compared with traditional integer differential equations, fractional differential calculus can better simulate the natural world because it is a quasi-differential operator with good memory and heredity as well as obvious non-locality. Some physical processes and