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In this paper, we aim to discuss a fractional complex Ginzburg–Landau equation by using the parabolic law and the law of weak non-local nonlinearity. Then, we derive dynamic behaviors of the given model under certain parameter regions by employing the planar dynamical system theory. Further, we apply the ansatz method to derive soliton, bright and kinked solitons and verify their existence by imposing certain conditions. In addition, we integrate our solutions in appropriate dimensions to explain their behavior at various groups of parameters. Moreover, we compare the graphical representations of the established solutions at different fractional derivatives and illustrate the impact of the fractional derivative on the investigated soliton solutions as well. [ABSTRACT FROM AUTHOR]

The fractional massive Thirring model is a coupled system of nonlinear PDEs emerging in the study of the complex ultrashort pulse propagation analysis of nonlinear wave functions. This article considers the NFMT model in terms of a modified Riemann–Liouville fractional derivative. The novel travelling wave solutions of the considered model are investigated by employing an effective analytic approach based on a complex fractional transformation and Jacobi elliptic functions. The extended Jacobi elliptic function method is a systematic tool for restoring many of the well-known results of complex fractional systems by identifying suitable options for arbitrary elliptic functions. To understand the physical characteristics of NFMT, the 3D graphical representations of the obtained propagation wave solutions for some free physical parameters are randomly drawn for a different order of the fractional derivatives. The results indicate that the proposed method is reliable, simple, and powerful enough to handle more complicated nonlinear fractional partial differential equations in quantum mechanics. [ABSTRACT FROM AUTHOR]