<p>This article presents a generalization of the entropy and its complementary measure, called generalized fractional extropy and entropy. We compare the two measures, highlight their features, and establish several bounds. Moreover, the approximation of the generalized fractional extropy is discussed. In addition, the differential generalized fractional extropy of its approximation is given. Finally, we demonstrate the application of the proposed measures in a pattern recognition problem, where the softmax function is employed.</p>