Applications of (h,q)-TimeScale Calculus to the Solution of Partial Differential Equations

In this article we developed the idea of q-timescale calculus in quantum geometry. It introduces the q time scale-integral operator and differential operator. Its analysis some derived significant principles and findings which follow the calculus of q-time scale comparing with the Leibnitz-Newton usual calculus. The operator Δ_q- differential reduced method of transformation is proposed to transform the partial differential equation problems to time scale by utilizing the partial -differential equations. With easily computable coefficients the solution is calculated in the version of a power series which is convergent. It is also illustrated the performance and effectiveness of the proposed procedure and applying some important examples of partial differential equations. The newly obtained solution can be merges with usual calculus if the values of the parameter is set in the partial differential equation. The finding of the present work is that the Δ_q- differential transformation reduced method is convenient and efficient to solve partial differential equations such as heat equation , Laplace and Bernoulli equation.