Title: Dynamic feedback control strategy of financial market based on fractional order differential equation

Authors: Qin Wang; Huwei Li; Bilal Alatas

Addresses: School of Economics, Zhongyuan University of Science and Technology, Zhengzhou 451400, Henan, China ' College of Intelligent Finance and Economics, Henan Economy and Trade Vocational College, Zhengzhou 450000, Henan, China ' Department of Software Engineering, Firat University, Türkiye

Abstract: In the face of increasingly complex and diverse financial markets, accurately identifying market fluctuations and effectively monitoring risks have become major challenges in financial regulation. Traditional differential equation models exhibit limitations when handling high-dimensional, nonlinear, and complex data. This paper introduces the A-TransHS framework, which integrates the strengths of differential equation-based prediction and deep learning technologies. It leverages the Transformer architecture's self-attention mechanism to extract temporal features from historical time series data and subsequently optimises the parameters of mixed sub-fractional order differential equations. Experimental results on the Yahoo Finance and CBOE datasets demonstrate that the A-TransHS framework significantly outperforms traditional methods and other deep learning models in terms of short- and long-term predictive accuracy, as measured by RMSE, MAE, and MAPE. These findings highlight its strong potential for modelling financial market dynamics and enhancing risk management.

Keywords: mixed sub-fractional order differential equations; financial regulation; option price prediction; transformer.

DOI: 10.1504/IJDSDE.2025.148521

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.3, pp.250 - 266

Received: 07 Mar 2025
Accepted: 21 Apr 2025
Published online: 10 Sep 2025 *

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