A New Concept for Fractional Quantum Calculus: (B; q)-Calculus and Its Properties

Abstract

In this article, authors expressed a new definition called (B; q)- derivative and integral which is a new type of fractional quantum derivative and integral. Also theorems and proofs on some basic properties of (B; q)- derivative and integral such as product rule, quotient rule, linearity and etc. are stated. These new definitions can be used in many different models arising in physical applications.