A POWERFUL ITERATIVE APPROACH FOR QUINTIC COMPLEX GINZBURG–LANDAU EQUATION WITHIN THE FRAME OF FRACTIONAL OPERATOR

Shao-Wen Yao (), Esin Ilhan (), P. Veeresha () and Haci Mehmet Baskonus
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Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China
Esin Ilhan: ��Kirsehir Ahi Evran University, Kirsehir, Turkey
P. Veeresha: ��Department of Mathematics, CHRIST (Deemed to be University), Bangalore 560029, India
Haci Mehmet Baskonus: �Faculty of Education, Harran University, Sanliurfa, Turkey

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-13

Abstract: The study of nonlinear phenomena associated with physical phenomena is a hot topic in the present era. The fundamental aim of this paper is to find the iterative solution for generalized quintic complex Ginzburg–Landau (GCGL) equation using fractional natural decomposition method (FNDM) within the frame of fractional calculus. We consider the projected equations by incorporating the Caputo fractional operator and investigate two examples for different initial values to present the efficiency and applicability of the FNDM. We presented the nature of the obtained results defined in three distinct cases and illustrated with the help of surfaces and contour plots for the particular value with respect to fractional order. Moreover, to present the accuracy and capture the nature of the obtained results, we present plots with different fractional order, and these plots show the essence of incorporating the fractional concept into the system exemplifying nonlinear complex phenomena. The present investigation confirms the efficiency and applicability of the considered method and fractional operators while analyzing phenomena in science and technology.

Keywords: Fractional Natural Decomposition Method; Caputo Derivative; Ginzburg–Landau Equation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400235

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