Discrete weighted fractional calculus and applications

We introduce fractional (nabla) sums and differences with a weight function and prove some of their properties. We give particular emphasis to the tempered fractional case. In the end, we postulate a novel entropic functional and discuss some of its properties.

Automated summary

This study introduces fractional (nabla) sums and differences with a weight function and proves some of their properties, with particular emphasis on the tempered fractional case. It also postulates a novel entropic functional and discusses some of its properties.