Neutral Delayed Fractional Models in Financial Time Series: Insights into Borsa Istanbul Sectors Affected by the Kahramanmaraş Earthquake

This study examines the impact of the Kahramanmaraş Earthquake on four key sectors of Borsa Istanbul: Basic Metal, Insurance, Non-Metallic Mineral Products, and Wholesale and Retail Trade using neutral delayed fractional differential equations. Employing the Chebyshev collocation method, we numerically solved the neutral delayed fractional differential equations with initial conditions scaled by each sector’s log difference standard deviation to accurately reflect market volatility. Fractional orders were derived from the Hurst exponent, and time delays were identified using average mutual information, autocorrelation function, and partial autocorrelation function methods. The results reveal significant changes post-earthquake, including reduced market persistence and increased volatility in the Basic Metal and Insurance sectors, contrasted by enhanced stability in the Non-Metallic Mineral Products sector. Neutral delayed fractional differential equations demonstrated superior performance over traditional models by effectively capturing memory and delay effects. This work underscores the efficacy of neutral delayed fractional differential equations in modeling financial resilience amid external shocks.