On q,ω -differential transform method

Abstract

In this study, the differential transform method (DTM) associated with the Hahn difference operator ( D q , ω ) has been examined. The definitions and theorems of the one and two-dimensional q , ω -DTM are introduced. Then, the presented q , ω -DTMs are applied to obtain the analytical or approximation solution of linear or non-linear q , ω -initial value problems consisting of the q , ω -ordinary or q , ω -partial differential equation.