We expand a new generalization of the two-dimensional DIFFERENTIAL trans-form method. The new generalization is based on the two-dimensional differ-ential TRANSFORM method, fractional power series expansions, and conformable fractional derivative. We use the new method for solving a nonlinear con-formable fractional partial DIFFERENTIAL equation and a system of conformable fractional partial DIFFERENTIAL equation. Finally, numerical examples are pre-sented to illustrate the preciseness and effectiveness of the new technique.

Introduction: The theory and application of linear and nonlinear delay DIFFERENTIAL equations is an important subject within physics and applied mathematics.There are several numerical approaches for solving linear and nonlinear delay DIFFERENTIAL equations.Aim: In this paper, DIFFERENTIAL TRANSFORM method (DTM) is applied to numerical solution of linear and nonlinear delay DIFFERENTIAL equations.Materials and Methods: In this work, we presented simple proofs of the DIFFERENTIAL TRANSFORM Theorems and then we applied them to solving linear and nonlinear delay DIFFERENTIAL equations.Results: Numerical results compared to exact solutions are reported and it is shown that DTM is a reliable tool for the solution of delay DIFFERENTIAL equations.Conclusion: The present method reduces the computational difficulties of the other traditional methods and all the calculations can be made simple manipulations. Several examples were tested by applying the DTM and the results have shown remarkable performance.

In this paper, we study the numerical solution of hybrid fuzzy DIFFERENTIAL equations by using DIFFERENTIAL TRANSFORMation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an in finite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM and Predictor corrector method (PCM), we have studied their accuracy.

This paper presents a class of theoretical and iterative method for linear partial DIFFERENTIAL equations.An algorithm and analytical solution with a initial condition is obtained using the reduced DIFFERENTIAL TRANSFORM method. In this technique, the solution is calculated in the form of a series with easily com-putable components. There test modeling problems from mathematical mechanic, physic, electronic and so on, and are discussed to illustrate the effectiveness and the performance of the our method.

The complexity of solving DIFFERENTIAL equations in real-world applications motivates researchers to extend numerical methods. Among different numerical and semi-analytical methods for solving initial and boundary value problems, the DIFFERENTIAL TRANSFORM method (DTM) has received no-table attention. It has developed and experienced generalizations for implementing other types of mathematical problems such as optimal control, calculus of variations, and integral equations. This review aims to provide insight into DTM. History, theoretical base, applications, computational aspects, and its revisions are reviewed. The present study helps to understand the theory, capabilities, and features of the DTM, as well as its drawbacks and limitations.