Dynamic study of Clannish Random Walker's parabolic equation via extended direct algebraic method

In this article, we present an idea to attain the variety of novel optical solitons solutions for nonlinear time-fractional Clannish Random Walker's parabolic (CRWP) equation in the manner of beta-derivative using a well-known analytical technique namely, extended direct algebraic method. A diversity of bright, singular, dark, periodic-singular and combo dark-bright solitons solutions are assembled in the shape of rational, hyperbolic and exponential functions. Some of the extracted results are sketched in the pattern of 3D, 2D and contour plots, for the purpose to demonstrate the physical behavior of the attained solutions. We also investigate the influence of the fractional order parameter on the obtained solutions which demonstrates how changes in this parameter affect the properties and behavior of the soliton solutions in the context of the time-fractional CRWP model. The novelty of the extracted solutions is determined by comparing with some other solutions which are already listed in the works for the CRWP equation, which shows the effectiveness and authenticity of the proposed method. The under consideration method is also utilized to any other nonlinear integer and fractional model appears in physics and engineering.