Variable fractional modeling of nonlinear Gilson–Pickering equation via discrete singular convolution method

Abstract This paper exposes the precise soliton solutions of constant and variable order fractional for nonlinear Gilson-Pickering equation (GPE) via a novel numerical technique for the first time. These techniques are polynomial differential quadrature and discrete singular convolution method combined with Caputo and generalized Caputo definition. These techniques are applied to convert NLPDEs into nonlinear ODEs to extract wave solutions. Hence, we have employed perturbation and iterative techniques to solve Nonlinear ODEs. Thus, MATLAB code is designed to derive the results of the given model. Moreover, a parametric analysis is offered to discover the effect of the presented techniques on soliton solutions. Finally, the obtained results from this article show that the presented method is preferred for successfully solving nonlinear PDEs that appear in mathematical physics.