Computational analysis of the third order dispersive fractional PDE under exponential-decay and Mittag-Leffler type kernels

This article aims to investigate the fractional dispersive partial differential equations (FPDEs) under non-singular and non-local kernels. First, we study the fractional dispersive equations under the Caputo-Fabrizio fractional derivative in one and higher dimension. Second, we investigate the same equations under the Atangana-Baleanu derivative. The Laplace transform has an excellent convergence rate for the exact solution as compared to the other analytical methods. Therefore, we use Laplace transform to obtain the series solution of the proposed equations. We provide two examples of each equation to confirm the validity of the proposed scheme. The results and simulations of examples show higher convergence of the fractional-order solution to the integer-order solution. In the end, we provide the conclusion and physical interpretation of the figures.