Zhou, ZizhaoAbbas, M. S.El-Rashidy, K.Qadri, Intakhab AlamAbuzar, MuhammadAkguel, AliHassani, Murad Khan2024-12-242024-12-2420241687-2770https://doi.org/10.1186/s13661-024-01941-4https://hdl.handle.net/20.500.12604/7305This paper analyses the analytical solutions of the fractional twin-core coupler (fTCC) equations, which include Kerr law nonlinearity, utilising the unified and sub-ODE methods along with beta and M-truncated fractional derivatives. The visually detailed report highlights certain solutions adorned with carefully selected parametric values to demonstrate their distribution. The main concept of this enhancement involves adopting a new formal structure for the preferred solution and considering the dynamic aspects of the problem. To achieve a more profound comprehension of physical implications of these solutions, we have depicted them through diverse visualisations, including 3D and 2D plots. Subsequently, a planar dynamical system is introduced, and bifurcation analysis is performed to determine the bifurcation structures of the nonlinear and super-nonlinear travelling wave solutions of the proposed model. Every potential phase portrait is displayed using specific parameter values. Finally, the model is transformed via the Galilean transformation into a planer dynamical system and the sensitivity performance is assessed.eninfo:eu-repo/semantics/openAccessBeta-derivativeM-truncated derivativeAnalytical solutionsUnified methodSub-ODE methodPhase portraitsSensitivity analysisArticle20241N/AWOS:001358869900001Q12-s2.0-8520967079610.1186/s13661-024-01941-4