<p>This paper presents a fractional-order economic production quantity (EPQ) model that incorporates memory effects, defective items, variable production costs, and promotion-dependent demand. In contrast to classical inventory models, which assume that product demand is memoryless, the proposed approach employs the Caputo fractional derivative to represent the influence of past decisions on current inventory dynamics. The model simultaneously determines the optimal production rate, production quantity, and maximum profit. A case study of a small-scale footwear manufacturing company is used to validate the results of the proposed model. The results demonstrate that incorporating memory effects provides more realistic insights into demand behavior and profitability. The sensitivity analysis emphasizes the important role of production cost parameters, defective items, and promotional efforts in determining profit outcomes. The managerial implications suggest that quality control, effective promotional strategies, and accurate cost management are essential to maximize profitability. The study indicates that the fractional-order model generalizes the classical case, offering a versatile and robust tool for decision-making in uncertain and competitive markets.</p>