In this paper, we have extended the Fractional Differential Transform method for the numerical solution of the system of fractional partial differential-algebraic equations. The system of partial differential-algebraic equations of fractional order is solved by the Fractional Differential Transform method. The results exhibit that the proposed method is very effective.

Determining the exact solution to the partial differential equations has been one of the most important concerns of scientists in the various centuries. This paper applies the generalized exponential rational function method to a new extension of nonlinear Schrödinger equation. Many new analytical solutions are retrieved by choosing suitable coefficients of parameters under different family cases. Some important surfaces of results such as the imaginary part, the real part, and their modulus are also depicted with the help computational packet program. According to the results obtained in this paper, the method can be assumed to be a suitable tool in solving differential equations.