Mathematics and Statistics Vol. 8(6), pp. 631 - 636
DOI: 10.13189/ms.2020.080602
Reprint (PDF) (462Kb)

Solution of Newell – Whitehead – Segal Equation of Fractional Order by Using Sumudu Decomposition Method

Shams A. Ahmed ^1,2,*, Mohamed Elbadri ^1,2
1 Department of Mathematics, Faculty of Sciences and Arts, Jouf University, Tubarjal, Saudi Arabia
² Department of Mathematics, University of Gezira, Sudan

ABSTRACT

Newell Whitehead Segal (NWS) equation has been used in describing many natural phenomena arising in fluid mechanics and hence acquired more attention. Studies in the past gave importance to obtaining numerical or analytical solutions of this kind of equations by employing methods like Modified Homotopy Analysis Transform method (MHATM), Adomian Decomposition method (ADM), Homotopy Analysis Sumudu Transform method (HASTM), Fractional Complex Transform (FCT) coupled with He's polynomials method (FCT-HPM) and Fractional Residual Power Series method (FRPSM). This research aims to demonstrate an efficient analytical method called the Sumudu Decomposition Method (SDM) for the study of analytical and numerical solutions of the NWS of fractional order. The coupling of Adomian Decomposition method with Sumudu transform method simplifies the calculation. From the numerical results obtained, it is evident that SDM is easy to execute and offers accurate results for the NWS equation than with other methods such as FCT-HPM and FRPSM. Therefore, it is easy to apply the coupling of Adomian Decomposition technique with Sumudu transform method, and when applied to nonlinear differential equations of fractional order, it yields accurate results.

KEYWORDS
Newell – Whitehead – Segal Equation, Sumudu Decomposition Method, Caputo Fractional Derivative

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Shams A. Ahmed , Mohamed Elbadri , "Solution of Newell – Whitehead – Segal Equation of Fractional Order by Using Sumudu Decomposition Method," Mathematics and Statistics, Vol. 8, No. 6, pp. 631 - 636, 2020. DOI: 10.13189/ms.2020.080602.

(b). APA Format:
Shams A. Ahmed , Mohamed Elbadri (2020). Solution of Newell – Whitehead – Segal Equation of Fractional Order by Using Sumudu Decomposition Method. Mathematics and Statistics, 8(6), 631 - 636. DOI: 10.13189/ms.2020.080602.