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

Suad Mohammed Hassan; Duaa Mohammed Hamid; Methaq Hamza Geem

doi:10.5269/bspm.77345

Suad 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

Abstract

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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References

ALQURAN, Marwan, et al, Promoted residual power series technique with Laplace transform to solve some timefractional problems arising in physics., Results in Physics. 19, 1-7, (2020).

Brian D.,Integral Transforms and their Applications. Springer,USA,554-589,(2002).

Hussain F.,Laplace Decomposition Method for the System of Linear and Non-Linear Ordinary . J.Differential Equations, Mathematical Theory and Modeling,5(12),124-135,(2015).

Gabriel N.,Ordinary Differential Equations. Mathematics De-partment, Michigan state University, East lansing. MI 48824,(2014).

Jafari H.,Yang X.,Towards new general double integral transform and its applications to differential equations. J.Mathematical Methods in the Applied Sciences,2021(1),1-8,(2021).

H.Gundo, O. Gozukızıl, Applications of the decomposition methods to some nonlinear partial differential equations. J.NTMSCI,6(3) ,57-66,(2018).

Y. AL-Ameri , M. H. Geem,On g-transformation . Journal of university of Babylon,Pure and applied sciences, Vol29(2),1-5,(2021).

M. H. Geem,On strongly continuous ρ h-semigroup. Journal of Physics(IOP): Conference Series, 1234(1),1-12,(2019).

M. H. Geem and A. M. Abbood,On α-g-Transformation and its properties. American Institute of Physics Conference Series,2834(1),1-9,(2023).

M. H. Geem , A.R. Hassan and H.I. Neamah,0-Semigroup of g-transformation. J. of Interdisciplinary Mathematics,28(1),311-316,(2025).

M. H. Geem, S. T. KhathemFractional h- Ilyas-Farid Integral and Derivative. J.AIP Conference Proceedings,7th International Conference of the Iraqi Academics Syndicate for Sciences (ICIASS),Iraq ,1-12,(2025).

A. Kumar, S. Kumar, and M. Singh,Residual power series method for fractional Sharma-Tasso-Olever equation. J.Commun. Numer. Anal,10,1-10,(2016).

M. I. Liaqat, A. Akg¨ul, and E. Y. Prosviryakov,An efficient method for the analytical study of linear and nonlinear time-fractional partial differential equations with variable coefficients. Bulletin of Samara State Technical University. Series Physical and Mathematical Sciences,27(2),214-240,(2023).

M. I. Liaqat, S. Etemad, and S. Rezapour,A novel analytical Aboodh residual power series method for solving linear and nonlinear time-fractional partial differential equations with variable coefficients. AIMS MathematicsAIMS MATHEMATICS,7(9),16917-1694,(2022).

R. Almeida,A Caputo fractional derivative of a function with respect to another function. Communications in Nonlinear Science and Numerical Simulation,44(1),460-481,(2017).

R. Almeida, A. B. Malinowska, and M. T. T. Monteiro,Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications. Mathematical Methods in the Applied Sciences,41(1),336-352,(2018).

D. S. Oliveira and E. Capelas de Oliveira,On a Caputo-type fractional derivative. Advances in Pure and Applied Mathematics,10(2),81-91,(2019).