Exact Solutions of M-fractional Complex Ginzburg-Landau Equation via Two Analytical Methods

Authors

Nematollah Kadkhoda, Department of Mathematics, Faculty of Engineering Science, Quchan University of Technology, Quchan, IranFollow
Mojtaba Baymani, Department of Mathematics, Faculty of Engineering Science, Quchan University of Technology, Quchan, IranFollow
Maad M. Mijwil, College of Administration and Economics, Al-Iraqia University, Baghdad, IraqFollow
Mostafa Abotaleb, School of Electronic Engineering and Computer Science, Department of System Programming, South Ural State University, 454080 Chelyabinsk, RussiaFollow

Abstract

This article investigates the M-fractional complex Ginzburg-Landau (CGL) equationby utilizing the modified simplest equation method and the modified G'G-expansion method. The CGL holds significant importance in the realm of oscillatory phenomena and optical fibers. By implementing a fractional complex transformation, the M-fractional CGL equation is transformed into an ordinary differential equation (ODE).By employing these methodologies, bright periodic solutions, periodic solutions, and dark wave solutions relevant to phenomena witnessed in nonlinear optics or plasma environments are ascertained.It is demonstrated that these methods are very powerful and efficient to solve many fractional differential equations.

Recommended Citation

Kadkhoda, Nematollah; Baymani, Mojtaba; Mijwil, Maad M.; and Abotaleb, Mostafa (2025) "Exact Solutions of M-fractional Complex Ginzburg-Landau Equation via Two Analytical Methods," Iraqi Journal for Computer Science and Mathematics: Vol. 6: Iss. 3, Article 11.
DOI: https://doi.org/10.52866/2788-7421.1267
Available at: https://ijcsm.researchcommons.org/ijcsm/vol6/iss3/11