Modeling Stock Market Recovery Dynamics Using Fractional Calculus

Understanding stock market recovery after financial crises remains a significant challenge for classical financial modeling approaches, which often fail to capture the memory-dependent and path-dependent nature of market behavior. This study proposes a fractional calculus-based framework for modeling the rehabilitation dynamics of stock markets, offering a more realistic representation of post-crisis recovery processes. By extending traditional differential equations to non-integer orders, the model incorporates historical dependence and long-range interactions inherent in financial systems. The rehabilitation process is characterized through key mechanisms including liquidity restoration, price momentum recovery, market sentiment adjustment, volatility reduction, price recovery, and price stabilization. These components collectively describe the gradual transition of the market from instability to equilibrium. The fractional-order formulation provides improved flexibility in capturing delayed responses and persistent effects observed in real trading environments. The results suggest that fractional calculus offers a robust mathematical tool for analyzing market resilience and behavioral adjustments of traders during recovery phases, thereby enhancing decision-making frameworks and reducing repetitive strategic errors in financial markets