New Analytical Solutions of Fractional Symmetric Regularized-Long-Wave Equation

Abstract

In this study, new extended direct algebraic method is successfully implemented to acquire new exact wave solution sets for symmetric regularized-long-wave (SRLW) equation which arise in long water flow models. By the help of Mathematica symbolic calculation package, the method produced a great number of analytical solutions. We also presented a few graphical illustrations for some surfaces. The fractional derivatives are considered in the conformable sense. All of the solutions were checked by substitution to ensure the reliability of the method. Obtained results confirm that the method is straightforward, powerful and effective method to attain exact solutions for nonlinear fractional differential equations. Therefore, the method is a good candidate to take part in the existing literature.

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

“…In the literature, rational (G /G)-expansion [14], new extended direct algebraic [18], improved Bernoulli subequation function [19], and modified extended tanh [20] methods include the conformable derivatives. 3 solutions which are trigonometric and hyperbolic are obtained by rational (G /G)-expansion method, 37 solutions which are rational, exponential, trigonometric and hyperbolic are obtained by new extended direct algebraic method, 3 solutions which are rational and exponential are obtained by improved Bernoulli sub-equation function method and 12 solutions which are trigonometric and hyperbolic are obtained by modified extended tanh method.…”

“…An important one of these equations is the fractional SRLW equation. So far, the solutions of the space-time fractional SRLW equation has been investigated by utilizing the sub-equation method [10], functional variable method [11], exp-function method [11], (G /G)-expansion method [11], tanh-coth method [2], tan-cot method [2], sech-csch method [2] and sec-csc method [2], a novel (G /G)-expansion method [12], Riccati equation method [13], rational (G /G)-expansion method [14], improved F -expansion method [15], the extended Jacobi elliptic function expansion method [16], the auxiliary equation method [17], new extended direct algebraic method [18], improved Bernoulli sub-equation function method [19], modified extended tanh method [20], rational exp(−Ω(η))-expansion method [21], (G /G, 1/G)-expansion method [22], extended auxiliary equation mapping method [23], (D α G/G)-expansion method [24], modified Kudryashov method [25], and the fractional (D α ξ G/G)-expansion method [26]. Among these methods, rational (G /G)-expansion, new extended direct algebraic, improved Bernoulli sub-equation function, and modified extended tanh methods include the conformable derivatives.…”

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

“…Furthermore, these can be utilized to estimate the boundary data that are used in numeric and semi-analytic methods. Such techniques include the Kudryashov method and its modifications [18][19][20], functional variable method [19], generalized Riccati equation mapping method [21], Jacobi elliptic function method [21,22], sine-Gordon expansion method [23], Hirota method [24], subequation method [25], soliton ansatz method [26], G /G-expansion method [27], new extended direct algebraic method [28], extended trial function method [29], new generalized exponential rational function method [30], integral dispersion equation method [31,32], modified extended tanh-function method [33], simple equation method [34,35], and modified simple equation methods [36] (see also the references that appear therein).…”

Optical solitons to a perturbed Gerdjikov-Ivanov equation using two different techniques

“…The analysis of such equations provides insightful physical information, useful for further applications. Many trails have been penned for the physical problems in the last years to get the analytical solutions of the NLPDEs with the recent computer technology [1][2][3][4][5][6][7][8][9][10][11][12]. A variety of powerful methods have been developed such as the exp(−φ(ζ))expansion expansion method [13,14], the (G /G)-expansion method [15,16], the new extended direct algebraic method [17,18], the first integral method [19,20], the extended Jacobi elliptic function expansion method [21,22], and so on [23][24][25][26][27][28][29][30].…”