This paper presents a novel neural network architecture called the flexible fractional wavelet neural network (FFrWNN), which enhances traditional wavelet networks by introducing two additional fractional wavelet parameters. These fractional parameters, along with the translation and scale parameters, are dynamically adjusted during the learning process, offering greater flexibility and improved approximation power. The network is trained using a stochastic gradient descent algorithm, and iterative online training formulas are developed for optimizing both the wavelet parameters and network weights. The stability of the network is proven through the Lyapunov stability approach, ensuring reliable convergence. The proposed FFrWNN is evaluated in the context of both one-dimensional and multi-dimensional dynamic system identification. Results demonstrate that the fractional wavelet parameters significantly improve the network's accuracy and efficiency. Compared to conventional neural networks, the FFrWNN shows superior performance in terms of precision and learning capability, making it a powerful tool for complex system modeling and signal processing applications.
Dadashzadeh, H. , Ahmadi, G. , Edrisi Tabrizi, Y. and Rezaei, B. (2025). Flexible fractional wavelet neural network for non-linear system identification. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.64339.2915
MLA
Dadashzadeh, H. , , Ahmadi, G. , , Edrisi Tabrizi, Y. , and Rezaei, B. . "Flexible fractional wavelet neural network for non-linear system identification", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.64339.2915
HARVARD
Dadashzadeh, H., Ahmadi, G., Edrisi Tabrizi, Y., Rezaei, B. (2025). 'Flexible fractional wavelet neural network for non-linear system identification', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.64339.2915
CHICAGO
H. Dadashzadeh , G. Ahmadi , Y. Edrisi Tabrizi and B. Rezaei, "Flexible fractional wavelet neural network for non-linear system identification," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.64339.2915
VANCOUVER
Dadashzadeh, H., Ahmadi, G., Edrisi Tabrizi, Y., Rezaei, B. Flexible fractional wavelet neural network for non-linear system identification. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.64339.2915
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