Approximate Analytical Solutions of Time Fractional Whitham–Broer–Kaup Equations by a Residual Power Series Method

Abstract

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham-Broer-Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is comparing the results with those of the Adomian decomposition method (ADM), the variational iteration method (VIM) and the optimal homotopy asymptotic method (OHAM). Illustrative examples reveal that the present technique outperforms the aforementioned methods and can be used as an alternative for solving fractional equations.

Least‐Squares Residual Power Series Method for the Time‐Fractional Differential Equations

“…And the least-squares residual power series method (LSRPSM) and the q-homotopy analysis method (q-HAM) [32] with u i (x, t) when i � 2 are compared with the classic residual power series method with u i (x, t) when i � 2, as shown in Table 3. e approximate solutions of the q-HAM can be written as 8 Complexity…”

“…In [7], the time-fractional foam drainage equation was worked out by the residual power series method. Wang and Chen [8] proposed that the residual power series can be applied to time-fractional Whitham-Broer-Kaup equations. e fractional variation of the (1 + 1)-dimensional Biswas-Milovic equation [9] was gured out by the residual power series method.…”

A fractional Whitham-Broer-Kaup equation and its possible application to Tsunami prevention

“…If u is the solution for a discontinuous medium, u0 is the solution for its continuous partner with same boundary and initial conditions. Whitham-Broer-Kaup (WBK) equation has been widely studied in solitary theory arising in shallow water [15,16], and its fractional partner describes shallow water in porous medium, which is used to absorb wave energy and prevent tsunami.…”

“…, -the height deviating from equilibrium position of liquid, and β and γ -the real constants that represent different diffusion powers. Fractional WBK equation with other fractional derivatives was studied in [15,16], this paper adopts the definition given in eq. (1).…”

A reliable technique for fractional modified Boussinesq and approximate long wave equations

“…These equations are studied by several authors via distinct techniques like, ADM [17], VIM [18], CFRDTM [15], LADM [19] and other techniques [20][21][22]. These cited techniques require huge computation and has highly complicated procedure to solve coupled systems.…”