q-Modified Differential Transform Method

Abstract

The modified or hybrid method is created by combining the differential transform method (DTM), Padé approximant, and Laplace transform. This method has been used frequently in many fields, especially in solving problems created by nonlinear equations. In this study, we examined the \(q\)-analog of this method. We define the method as the \(q\)-modified differential transformation method (\(q\)-MDTM). By creating \(q\)-analogs of some problems solved by Laplace transform and DTM in the literature, we are solving them with \(q\)-MDTM. In this sense, the study is an example of creating nonlinear \(q\)-differential equations and solving them by applying the \(q\)-modified method.