A Modified Differential Transform Method for Solving Nonlinear Systems

Abstract

Many natural phenomena are now being modelled by fractional calculus, however, there is still need for improvements of the present numerical approaches due to the non-local property of the fractional derivative and difficulty in solving problems related to physical units. In this paper, we present an improved numerical method based on Newton-Raphson fractional method (NFM) for solution of some nonlinear systems in complex space. Unlike in the Newton-Raphson fractional method, the commands of fractional derivatives are replaced with functions which is valid for one and several variables. The conformable fractional derivative of fractional order  was employed to replace the first order derivative in the Newton method. Numerical results have been presented which show that the proposed numerical approach is efficient and promising.