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In this paper, the perturbed and unperturbed fractional regularized long wave (FRLW) equation is taken into consideration by using analytical and numerical approaches. For the unperturbed considered model diverse solitonic structures are measured using two finest approaches which are extended (G′G2)-expansion method and the direct algebraic method. Then, the discussed equation is transformed into the planer dynamical system by using Galilean transformation. All possible types of phase portraits are plotted in the respect of the parameters. Also, the effect of physical parameters is observed after applying an extrinsic periodic power, then the responsive analysis is applied to evaluate the periodic and quasi-periodic behavior for distinct initial value problems. On some of that, multistability analysis is applied and it is observed that for some values of physical parameters of the discussed equation is multistable.