An entropy based on a fractional difference operator

In this work, we postulate a novel entropy functional, which depends on two parameters. This is motivated by the use of a certain fractional difference operator. We show that our entropy functional reduces to well-known ones for certain values of the parameters. Moreover, we discuss the Shannon-Khinchin axioms and the Lesche stability for this system.

Automated summary

In this work, a novel entropy functional is proposed, depending on two parameters and inspired by a specific fractional difference operator. It is shown that the entropy functional simplifies to well-known ones under certain parameter values, and the Shannon-Khinchin axioms and Lesche stability for this system are discussed.