Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

This work searches the new wave solutions of the time-fractional ion sound and Langmuir waves (ISLWs) equation and the time-fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation with the conformable derivative. The \(\left( m+\frac{1}{G^\prime }\right)\)-expansion method is employed for these models for the first time. Getting support from symbolic software, some new solutions are presented, which will be constructive for studies in the field of nonlinear physical phenomena. New wave solutions obtained by using the \(\left( m+\frac{1}{G^\prime }\right)\)-expansion method have applications in engineering, physics, and other scientific fields. The regarded method may provide a framework for the exact solutions of several evolution equations in applied sciences. Moreover, the graphical illustrations are also demonstrated to observe the dynamical behaviours of the solutions, which may benefit the development of new technologies.

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.

This study introduces a novel approach for analyzing the dynamic interplay among key economic indicators by employing a Caputo Fractional Fisher Information framework combined with partial information decomposition. By integrating fractional derivatives into traditional Fisher Information metrics, our methodology captures long-range memory effects that govern the evolution of monetary policy, credit risk, market volatility, and inflation, represented by INTEREST, CDS, VIX, CPI, and PPI, respectively. We perform a comprehensive comparative analysis using rolling-window estimates to generate Caputo Fractional Fisher Information values at different fractional orders alongside the memoryless Ordinary Fisher Information. Subsequent correlation, cross-correlation, and transfer entropy analyses reveal how historical dependencies influence both unique and synergistic information flows between indices. Notably, our partial information decomposition results demonstrate that deep historical interactions significantly amplify the informational contribution of each indicator, particularly under long-memory conditions, while the Ordinary Fisher Information framework tends to underestimate these synergistic effects. The findings underscore the importance of incorporating memory effects into information-theoretic models to better understand the intricate, time-dependent relationships among financial indicators, with significant implications for forecasting and policy analysis.