Numerical solutions of wavelet neural networks for fractional differential equations
Mingqiu Wu, Jinlei Zhang, Zhijie Huang, Xiang Li, Yumin Dong
Source 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.
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