The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches

• Published in: Results in physics 2023-09, Vol.52, p.106775, Article 106775
• Main Authors: Ehsan, Haiqa, Abbas, Muhammad, El-Rahman, Magda Abd, Ali, Mohamed R., Hendy, A.S.
• Format: Article
• Language: English
• Subjects: Beta-derivative; Conformable derivative; Fractional complex coupled maccari system; M-truncated derivative; Modified auxiliary equation method; Riccati–Bernoulli sub-ODE method
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2023.106775

In this work, the modified auxiliary equation method (MAEM) and the Riccati–Bernoulli sub-ODE method (RBM) are used to investigate the soliton solutions of the fractional complex coupled maccari system (FCCMS). Nonlinear partial differential equations (NLPDEs) can be transformed into a collection of algebraic equations by utilizing a travelling wave transformation, the MAEM, and the RBM. As a result, solutions to hyperbolic, trigonometric and rational functions with unconstrained parameters are obtained. The travelling wave solutions can also be used to generate the solitary wave solutions when the parameters are given particular values. There are several solutions that are modelled for different parameter combinations. We have developed a number of novel solutions, such as the kink, periodic, M-waved, W-shaped, bright soliton, dark soliton, and singular soliton solution. We simulate our figures in Mathematica and provide many 2D and 3D graphs to show how the beta derivative, M-truncated derivative and conformable derivative impacts the analytical solutions of the FCCMS.The results show how effectively the MAEM and RBM work together to extract solitons for fractional-order nonlinear evolution equations in science, technology, and engineering. •Dynamical behaviour variation of fractional complex coupled maccari system is noted.•Two reliable and useful analytical approaches are used for solitary wave solutions.•Beta-derivative, M-truncated derivative and conformable derivative are used to understand their dynamical behaviour.•Dark, bright, periodic, and solitary wave solitons are obtained.•2D and 3D Fractional impact of the above derivatives on the physical phenomena is noted.