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