A Novel Approach using Residual Power series Method for solving nonlinear fractional partial differential equation

This paper aims to introduce modified method for residual power series method (RPSM) by combing with a novel transformation , namely gmn-transformation which is generalized for many integral transformations like Laplace , Fourier, Elzaki and others. Also, a new approach is based on Residual power series method and proposed formula for residual power series . MRPSM is stand for a novel Approach, this method to reduce the steps of the method RPSM and improves accuracy . Also by using gmn-transformation MRPSM is considered generalized for many methods which use different transformations like laplace, Elzaki and others transformations. We deal an import fractional pde equation , Newell-Whithead-Segel equation . In this paper , we introduce a general solution of general form for this equation and also some propositions , example and theorem are given.