Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives

Abstract

In this paper, we employ a sub-equation method to nd the exact solutions to the fractional (1 + 1) and (2 + 1) regularized long-wave equations which arise in several physical applications, including ion sound waves in plasma, by using a new de nition of fractional derivative called conformable fractional derivative. The presented method is more e ective, powerful, and straightforward and can be used for many other nonlinear partial fractional di erential equations.

A new analysis for fractional model of regularized long‐wave equation arising in ion acoustic plasma waves

“…The RLW equation of integer or fractional orders has been examined by putting up various techniques [13][14][15][16][17] with their own weakness and shortcomings such as huge computational work and takes much high time. In 1992, Liao put up an analytic technique known as homotopy analysis method (HAM) [18][19][20] for handling nonlinear problems.…”

A Collocation Method for Solving Fractional Order Linear System

“…where c [1,2], [2,3] and use algorithm 3.4, the error at time t = 1, 2 and 3 is 9.1359e − 07, 6.7420e − 05 and 0.0014, respectively. This example confirms Lemma 3.2, and so we see that algorithm 3.4 is useful.…”

“…The field of fractional differential equations has received attention and interest only in the past 20 years or so [2,4,3]. In recent years, studies concerning the application of the fractional differential equations in science has attracted more interest among scholars [9,5]; readers can refer to [7,8] for the theory and applications of fractional calculus in this regard.…”

Exact Solutions of a Family of Higher-Dimensional Space-Time Fractional KDV-Type Equations

“…Therefore, the efficient approaches to construct the solutions of FPDEs have attracted great interest by several groups of researchers. A large collection of analytical and computational methods has been introduced for this reason, for example the exp-function method [3,4], Adomian decomposition method [5], the ( / ) G G ′ -expansion method [6], the first integral method [7,8], the variational iteration method [9], the subequation method [10,11], the modified simple equation method [12], Jacobi elliptic function expansion method [13], the generalized Kudryashov method [14,15] and so on. One of the most powerful methods for seeking analytical solutions of nonlinear differential equations is the functional variable method, which was first proposed by Zerarka et al [16,17] in 2010.…”