Fig. 1

The dark soliton solution of Eq.(5.4) is illustrated in the form of 3D surface, 2D profile (fractional derivative impact) and contour representation for different parameter values i.e \(\sigma = 1,\ \delta = 2.5,\ \lambda = 1,\ \rho = 1,\ \alpha = 0.5,\ \theta = -1,\ \tau = 3,\ c = 1,\ \beta = \frac{1}{2}\), and \(\epsilon = 0.2\).