Fractal and Fractional (Jul 2024)
Employing the Laplace Residual Power Series Method to Solve (1+1)- and (2+1)-Dimensional Time-Fractional Nonlinear Differential Equations
Abstract
In this paper, we present a highly efficient analytical method that combines the Laplace transform and the residual power series approach to approximate solutions of nonlinear time-fractional partial differential equations (PDEs). First, we derive the analytical method for a general form of fractional partial differential equations. Then, we apply the proposed method to find approximate solutions to the time-fractional coupled Berger equations, the time-fractional coupled Korteweg–de Vries equations and time-fractional Whitham–Broer–Kaup equations. Secondly, we extend the proposed method to solve the two-dimensional time-fractional coupled Navier–Stokes equations. The proposed method is validated through various test problems, measuring quality and efficiency using error norms E2 and E∞, and compared to existing methods.
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