An entropy based on a fractional difference operator

Abstract

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.

Keywords:

• Generalized entropy
• fractional difference operator
• stability

2010 Mathematics Subject Classifications:

• 82A05
• 94A17

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Stimulus of Scientific Employment, Individual Support-2017 Call” with reference CEECIND/00640/2017.