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This article investigates the accuracy of the obtained analytical solutions of the nonlinear fractional Ostrovsky (NLFO.) equation. The researched solutions are obtained by exploiting the well-known generalized Tanh–function (GTF.) method with the Atengana– conformable fractional (ACF.) derivative in the wave transformation. Five–numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B-Spline (CBS), extended cubic B-Spline (ECBS), and exponential cubic B-Spline (ExCBS)) handle these solutions to check their solutions. The investigated fractional model is a general form of the KdV equation; however, the KdV equation’s solutions replace this effect with radiating inertia gravity waves. This model also describes a weak description of nonlinear ocean wave processes considering Earth rotation. The obtained analytical and numerical results are sketched through Mathematica 12 in different plot types to explain the waves’ dynamical behavior. Additionally, the computational obtained solutions’ stability is investigated. Finally, the paper’s contribution and obtained results’ novelty are demonstrated by comparing our solutions with those that have been obtained in previous scientific articles.

This paper deals with the numerical solution utilizing local version of the meshless collocation method for time-fraction Korteweg de Vries, Burgers’ and Korteweg de Vries-Burgers’ equations. This technique generates sparse and well-conditioned coefficient matrices when applied on a set of uniform or scattered nodes. To check the accuracy of the proposed local meshless technique three test problems are solved numerically.

The perturbed nonlinear Schrodinger–Hirota equation with spatio-temporal dispersion (PNSHE-STD) which governs the propagation of dispersive pulses in optical fibers, is investigated in this study using an improved Sardar sub-equation method. The Kerr and power laws of nonlinearity are taken into account. As a result of this improved technique, many constraint conditions required for the existence of soliton solutions emerge. We retrieved several solutions such as the bright solitons, dark solitons, singular solitons, mixed bright–dark solitons, singular-bright combo solitons, periodic, and other solutions. Furthermore, we demonstrate the dynamical behaviors and physical significance of these solutions by using different parameter values.