Application Of q-Calculus In Quantum Geometry

ABSTRACT

Every geometry is associated with some kind of space. Non-commutative geometry or quantum geometry deals with quantum spaces, including the classical concept of space as a very special case. We consider in particular the case that deals with calculus without limits (quantum calculus); employing the basic governing rules to obtain the q-derivative of some standard functions such as the trigonometric, exponential, logarithmic and hyperbolic functions. We discover that the q-derivative of these functions collapse naturally to the Newton-Leibnitz derivatives. We also considered q-integral which is the inverse of the q-derivative. The Reduced q-Differential Transform Method is presented for solving Partial q-Differential Equations, and the result obtained shows that this iteration procedure is less complicated and efficient when compared with the classical means of obtaining the analytical solution.