An Entropy Formulation Based on the Generalized Liouville Fractional Derivative

Abstract

This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series.

Keywords

• fractional derivatives
• fractional calculus
• entropy