Numerical solutions of wavelet neural networks for fractional differential equations

被引：14

作者：

Wu, Mingqiu ^{[1
]}

Zhang, Jinlei ^{[1
]}

Huang, Zhijie ^{[1
]}

Li, Xiang ^{[1
]}

Dong, Yumin ^{[1
]}

机构：

[1] Chongqing Normal Univ, Coll Comp & Informat Sci, Chongqing 401331, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 03期

基金：

中国国家自然科学基金;

关键词：

approximate solutions; fractional differential equations; numerical solutions; wavelet neural networks; VARIATIONAL ITERATION METHOD; HOMOTOPY PERTURBATION METHOD;

D O I：

10.1002/mma.7449

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 xNx 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.

引用

页码：3031 / 3044

页数：14