Application of the Laplace least square residual power series method to fractional KdV, CRD, and Burgers’ equations

This paper will use Laplace least square residual power series method (LLSRPSM) on nonlinear fractional partial differential equations, in particular, Korteweg–de Vries (KdV) equation, convection-reaction-diffusion (CRD) equation and the system of Burgers’ equations. The proposed method standardizes the descendants of the Laplace transform, the residue power series, and the least-square middleweight to come up with effective and accurate approximations of the solutions of the fraction-order. They compare the results of their findings with the available methods, the Yang transform homotopy perturbation method (YTHPM), the modified generalized Taylor fractional series method (MGTFSM), the Elzaki transform decomposition method (ETDM) and the Laplace residual power series method (LRPSM). It was compared to the competing methods that LLSRPSM is less erroneous and more stable and faster in convergence than the competing methods. Besides, the significance of fractional order parameter, Omega, is mentioned since a smaller value corresponds to the presence of memory and diffusion anomalies whereas larger values are expected to converge to the classical integer-order solutions. Overall, the findings support the effectiveness and relevance of LLSRPSM to nonlinear fractional PDEs that have the potential to find wide uses in physical and engineering sciences.