Solving Nonlinear Fractional PDEs with Applications to Physics and Engineering Using the Laplace Residual Power Series Method

Abstract

The Laplace residual power series (LRPS) method uses the Caputo fractional derivative definition to solve nonlinear fractional partial differential equations. This technique has been applied successfully to solve equations such as the fractional Kuramoto–Sivashinsky equation (FKSE) and the fractional generalized regularized long wave equation (GRLWE). By transforming the equation into the Laplace domain and replacing fractional derivatives with integer derivatives, the LRPS method can solve the resulting equation using a power series expansion. The resulting solution is accurate and convergent, as demonstrated in this paper by comparing it with other analytical methods. The LRPS approach offers both computational efficiency and solution accuracy, making it an effective technique for solving nonlinear fractional partial differential equations (NFPDEs). The results are presented in the form of graphs for various values of the order of the fractional derivative and time, and the essential objective is to reduce computation effort.