Fractional Calculus; Loss Function; Grünwald-Letnikov Derivative

This paper presents a new method of creating neural networkloss functions using the concepts of fractional calculus. By integratingnon-integer order derivatives, we transform conventional loss functionsinto fractional models, such as fractional Mean Squared Error, fractionalHuber loss, and fractional cross-entropy. We provide both theoreticalframeworks and empirical evidence across classification and regressionbenchmarks, emphasizing performance enhancements and practical considerations.