Abstract
The current manuscript investigates the fractal model of the complex Ginzburg Landau equation which has many applications in fiber optics. The two algorithms namely, the semi-inverse approach and Painlevé method is adopted to uncover the soliton solutions of the governing system. The proposed techniques are more straightforward, succinct, accurate, and simple to calculate. As a result, bright and kink solitons are retrieved by the implementation of above-mentioned strategies. The constraint conditions that assure the presence of these solitons appear from the solutions of the model. Due to fractal dimension value irregularity and spikes appear in the solutions which are depicted by graphical illustrations. For several values of fractal parameter 2D, 3D and density plots are presented for the outcomes of semi-inverse strategy and 3D graphs are depicted for Painlevé approach. These techniques proven to be very useful and efficient gadgets for solving nonlinear fractal differential equations that emerge in mathematical physics.