Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

Abstract

We apply the functional variable method, exp-function method, and(G′/G)-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE) in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

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

“…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.…”

Pure Traveling Wave Solutions for Three Nonlinear Fractional Models

“…The functional variable method, exp-function method, and ðG ′ /GÞ-expansion method to the fractional SRLW equation in the sense of the modified Riemann-Liouville derivative were utilized in Ref. [35]. The interested readers can see more works in Refs.…”

Application of two different algorithms to the approximate long water wave equation with conformable fractional derivative

“…In order to solve the nonlinear fractional partial differential equations, a general method cannot be defined so far. Also, in recent years, several effective methods have been applied to obtain exact solutions of these equations such as sub-equation method (Alzaidy, 2013;Mohyud-Din, Nawaz, Azhar, & Akbar, 2017;, tanh method , simplest equation method (Taghizadeh, Mirzazadeh, Rahimian, & Akbari, 2013), Jacobi elliptic function expansion method , Kudryashov method (Demiray, Pandir, & Bulut, 2014;Eslami, 2016;Hosseini, Mayeli, & Ansari, 2017;Sonmezoglu, Ekici, Moradi, & Zhou, 2017), trial equation method (Ekici et al, 2016;Odabasi & Misirli, 2015;Pandir, Gurefe, & Misirli, 2013), exp-function method (Bekir, Guner, Aksoy, & Pandir, 2015;Zhang et al, 2010), first integral method (Eslami, Fathi, Mirzazadeh, & Biswas, 2014;Eslami & Rezazadeh, 2016;Younis, 2013), (G 0 /G)-expansion method (Ray & Sahoo, 2017), modification of the truncated expansion method (Mirzazadeh & Eslami, 2013), functional variable method (Bekir, Guner, Bhrawy, & Biswas, 2015), variable separation method (Wang & Dai, 2015;Wang, Zhang, & Dai, 2016), modified tanh-function method , Laplace transform method , homotopy analysis method , ansatz method (Zayed & Al-Nowehy, 2017) and so on (Biswas, Bhrawy, Abdelkawy, Alshaery, & Hilal, 2014;Guner & Eser, 2014;Korkmaz, 2017;Mirzazadeh, 2016;Mirzazadeh & Eslami, 2013;Saqib et al, in press;Sheikh et al, 2016).…”