Neural network has good self-learning and adaptive capabilities. In this paper, a wavelet neural network is proposed to be used to solve the value problem of fractional differential equations (FDE). We construct a wavelet neural network (WNN) with the structure 1 ×N× 1 based on the wavelet function and give the conditions for the convergence of the given algorithm. This method uses the truncated power series of the solution function to transform the original differential equation into an approximate solution, then, using WNN, update the parameters, and finally get the FDE solution. Simulation results prove the validity of WNN.

中文翻译：

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分数阶微分方程小波神经网络的数值解

神经网络具有良好的自学习和自适应能力。在本文中，提出了一种小波神经网络来解决分数阶微分方程（FDE）的取值问题。我们基于小波函数构造了一个结构为1×N×1的小波神经网络(WNN)，并给出了给定算法收敛的条件。该方法利用解函数的截断幂级数将原微分方程转化为近似解，然后利用WNN更新参数，最终得到FDE解。仿真结果证明了WNN 的有效性。