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ARTICLE

Regarding Deeper Properties of the Fractional Order Kundu-Eckhaus Equation and Massive Thirring Model

Yaya Wang¹, P. Veeresha², D. G. Prakasha³, Haci Mehmet Baskonus^4,*, Wei Gao⁵

1 Department of Information Engineering, Binzhou Polytechnic, Binzhou, 256603, China
2 Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India
3 Department of Mathematics, Davangere University, Shivagangothri, Davangere, 577007, India
4 Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, 63050, Turkey
5 School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, China

* Corresponding Author: Haci Mehmet Baskonus. Email:

(This article belongs to the Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2022, 133(3), 697-717. https://doi.org/10.32604/cmes.2022.021865

Received 10 February 2022; Accepted 11 April 2022; Issue published 03 August 2022

Abstract

In this paper, the fractional natural decomposition method (FNDM) is employed to find the solution for the KunduEckhaus equation and coupled fractional differential equations describing the massive Thirring model. The massive Thirring model consists of a system of two nonlinear complex differential equations, and it plays a dynamic role in quantum field theory. The fractional derivative is considered in the Caputo sense, and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique. In order to illustrate and validate the efficiency of the future technique, we analyzed projected phenomena in terms of fractional order. Moreover, the behaviour of the obtained solution has been captured for diverse fractional order. The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.

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Keywords

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