TITLE:
Application of q-Calculus to the Solution of Partial q-Differential Equations
AUTHORS:
Maliki Olaniyi Sadik, Bassey Okpo Orie
KEYWORDS:
q-Differential, q-Integral Operators, RqDTM Method, Initial Value Problem, Partial Differential Equation, MathCAD 14
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.8,
August
13,
2021
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.