Numerical solutions of wavelet neural networks for fractional differential equations. (6th May 2021)

• Record Type: Journal Article
• Authors: Wu, Mingqiu; Zhang, Jinlei; Huang, Zhijie; Li, Xiang; Dong, Yumin
• Other Names: Gao Feng guestEditor.; Feng Wenying guestEditor.; Zhang Xinguang guestEditor.; Ge Fudong guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 3(2023)
• Page Start: 3031
• Page End: 3044
• Publication Date: 2021-05-06
• Subjects: approximate solutions -- fractional differential equations -- numerical solutions -- wavelet neural networks; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7449
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.