Abstract
We introduce the concept of q-calculus in quantum geometry. This involves the q-differential and q-integral operators. With these, we study the basic rules governing q-calculus as compared with the classical Newton-Leibnitz calculus, and obtain some important results. We introduce the reduced q-differential transform method (RqDTM) for solving partial q-differential equations. The solution is computed in the form of a convergent power series with easily computable coefficients. With the help of some test examples, we discover the effectiveness and performance of the proposed method and employing MathCAD 14 software for computation. It turns out that when q = 1, the solution coincides with that for the classical version of the given initial value problem. The results demonstrate that the RqDTM approach is quite efficient and convenient.
Highlights
Every physical theory is formulated in terms of mathematical objects
We introduce the concept of q-calculus in quantum geometry
We introduced the concept of q-calculus in quantum geometry
Summary
Every physical theory is formulated in terms of mathematical objects. It is necessary to establish a set of rules to map physical concepts and objects into mathematical objects that we use to represent them. We discover that this operator algebra [3] [4] [5] forms some kind of noncommutative geometric space This is in contrast to algebraic geometry [6] [7], which is built on a correspondence between spaces and commutative algebras. This correspondence in particular associates with any given space, the algebra of functions on it, and geometric notions are expressed in a purely algebraic format. In 2014, Maliki et al [9], discussed the notion of q-deformed calculus in quantum geometry They showed that the mathematical study of noncommutative geometry is intimately related to the so-called q-calculus, which is a generalization of the Newton-Leibnitz classical calculus. We summarize some important q-calculus results which will enable us to study non-commutative differential equations, we shall employ the reduced q-differential transform method (RqDTM) to solve partial q-differential equations
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