Comprehensive soliton solutions of fractional stochastic Kraenkel–Manna–Merle equations in ferromagnetic materials

Abstract

The inner characteristics of numerous nonlinear phenomena that arise in real-life problems are stated through nonlinear partial differential equations. This exploration is conducted with fractional stochastic Kraenkel–Manna–Merle model in ferromagnetic materials and achieved ample soliton solutions by adapting enhanced rational (G′/G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({G}^{\\prime}/G)$$\\end{document}-expansion and improved tanh schemes. Ferromagnetic materials play a vital role in telecommunications applications, data storage, and manipulation. A new wave variable in the sense of confirmable fractional derivative is utilized to convert the governing model into the ordinary system. The motions of ultra-short-wave pulses in ferrite’s materials are analyzed by showing the effects of fractional derivatives and noise terms on the Brownian motion through multiple diverse 3D, 2D and contour plots. Periodic, singular periodic, kink, anti-kink etc. are visualized under the different parameter’s values involved in the obtained solitary wave solutions. The outcomes made available in the current study might play vital role to depict relevant intricate nonlinear phenomena and inspire the researchers to consider the utilized techniques in further studies.