This paper aims to uncover fairly interesting optical soliton solutions in (2+1)-dimensions. The fractional temporal Kundu-Mukherjee-Naskar (KMN) equation is reviewed as a governing model. Local M-derivative along with the unified approach is used to acquire these soliton solutions. The predicted solutions are yielded with the constraint conditions and highlighted by their graphical portrayal. Lastly, the inuence of a local fractional parameter upon predicted solutions are depicted through 2D and 3D graphs.

This paper introduces the fractal Kraenkel-Manna-Merle (KMM) system, that explains nonlinear short wave propagation with zero conductivity for saturated ferromagnetic materials in an external field. The semi inverse technique and the new auxiliary equation method (NAEM) are used to generate a new set of solutions. The proposed methods are more straightforward, succinct, accurate, and simple to calculate dual mode solitary wave solutions. A collection of exact soliton solutions specifically bright, dark, singular-shaped and singular-periodic are generated. The estimated solutions are obtained using constraint conditions and are displayed through 2D, 3D and contour plots with appropriate parametric values. The arbitrary functions in the solutions are chosen as unique functions to generate some novel soliton structures.