A new concept of q-calculus with respect to another function

Abstract

In this paper, we present an approach to quantum calculus and its applications through a functional method. This approach enables the exploration of the number-theoretic properties of q-calculus in a functional framework, facilitating the modification of variable-order q-differential equations and their solutions. The paper primarily focuses on the functional aspects of quantum number theory, functional-order q-derivatives, and their applications.

Keywords

• q - Identities, q-calculus, Hypergeometric functions