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

suaad mohammed Hassan; Duaa Mohammed Hamid; Methaq Hamza Geem

doi:10.5269/bspm.77345

suaad mohammed Hassan Iraqi minstry of Education https://orcid.org/0009-0001-7707-4310
Duaa Mohammed Hamid Al-Qadisiyah university https://orcid.org/0009-0008-5258-1798
Methaq Hamza Geem Al-Qadisiyah university https://orcid.org/0000-0002-8932-9296

Résumé

This paper aims to introduce modified method for residual power series method (RPSM) by combing with a novel transformation , namely g_mn-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 g_mn-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.

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