Differential transform method and its applications to some engineering problems

This study consists of six chapters. In the first chapter, the definitions of one and more dimensional transformations of the differential transformation method are given. In the second chapter, some of the basic theorems of differential transformations such as summations, differences, multiplication with constant and derivatives of analytic functions are presented. In the third chapter, the applications of differential transformation method is applied to the partial differential equations are shown. In the fourth chapter, the fractional differential transformation method which is developed for fractional differential equations is presented. On the other hand, the definition of Riemann Liouville's and Caputo's fractional derivatives are presented and Adomian's polynomials are defined which plays an important role in the differantial transformation of nonlinear terms. In the fifth chapter, the applications of the nonlinear fractional ordinary and partial differential equations are considered. This method is also applied to the which is well-known in the literature Bratu type differential equations and biological population equations. At last the numerical solutions sketched by graphs and shown with graphs and tables. In the last chapter, conclusions and suggestions are presented.