Proposal for the Application of Fractional Operators in Polynomial Regression Models to Enhance the Determination Coefficient $R^2$ on Unseen Data

Since polynomial regression models are generally quite reliable for data with a linear trend, it is important to note that, in some cases, they may encounter overfitting issues during the training phase, which could result in negative values of the coefficient of determination $R^2$ for unseen data. For this reason, this work proposes the partial implementation of fractional operators in polynomial regression models to generate a fractional regression model. The goal of this proposal is to attempt to mitigate overfitting, which could improve the value of the coefficient of determination for unseen data, compared to the polynomial model, under the assumption that this would contribute to generating predictive models with better performance. The methodology for constructing these fractional regression models is detailed, and examples applicable to both Riemann-Liouville and Caputo fractional operators are presented.