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.