Fractional order models for soybean drying kinetics: A mathematical approach

Abstract This study presents an advanced mathematical modelling approach to analyze the drying kinetics of Monsoy 6410 soybeans at temperatures of 50, 60, 70, and 80°C. Experimental data were obtained using a fixed‐bed dryer. Classical drying models were evaluated and compared with the Friesen fractional‐order model, which was enhanced by introducing a moisture‐dependent kinetic constant k ( X ). The modelling was performed using R software. Statistical comparisons using Akaike information criterion (AIC), Bayesian information criterion (BIC), mean squared error (MSE), and root mean squared error (RMSE) demonstrated the superiority of the fractional‐order models over classical ones. For example, at 50°C, the fractional‐order model with linear k(X) achieved AIC = −374, MSE = 6.98 × 10 −8 , and RMSE = 2.64 × 10 −4 , outperforming the Verma model (AIC = −342, RMSE = 4.55 × 10 −4 ). Across all temperatures, the fractional model with linear k(X) provided the best fit in 3 of 4 cases. This confirms the model's ability to capture complex drying behaviour more accurately, especially at high temperatures, where non‐linear and memory effects are significant. The results demonstrate the importance of fractional calculus in improving drying kinetics modelling and optimizing agro‐industrial drying processes.