This work presents a family of \(\alpha \) -order curves based on the error function, derived from the Maclaurin series expansion and the Lacroix definition of the fractional derivative. The model uses fractional derivative orders in the interval \(0 < \alpha \le 1\) , with a local and adaptive optimization of \(\alpha \) through sliding windows. The methodology was validated using real photovoltaic panel efficiency data from a clear day in Bucaramanga, Colombia, capturing typical diurnal variations. The results show that the optimal fractional order \(\alpha \) varies throughout the day, from approximately 0.37 in the late afternoon to 0.91 during peak irradiance, reflecting the system’s dynamic memory effects. The proposed model accurately reproduces the morning rise, midday peak, and afternoon decline in efficiency, achieving average RMSE and MAE values of 0.0083 and 0.0068, respectively. These findings suggest that fractional calculus with adaptive \(\alpha \) provides a flexible and accurate framework for modeling photovoltaic efficiency, capturing transient and historical dependencies that traditional integer-order models fail to represent adequately.