The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation

Abstract

The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of .

New Hyperbolic Function Solutions for Some Nonlinear Partial Differential Equation Arising in Mathematical Physics

“…We have obtained the tangent hyperbolic function solution ( ) 4 , u x t , hyperbolic function solutions such as ( ) 1 , u x t and ( ) , u x t for the (1 + 1)-dimensional nonlinear DMBBME by using GKM, which is a special case of the transformed rational function method [8]. …”

“…better understanding of such natural phenomena are possible with the help of analytical investigations obtained by using various methods such as trial equation method, modified trial equation method, the Sine-Cosine and the exp-function methods, the tanh method, the exp-function method [1][2][3][4][5][6][7], the transformed rational function method [8], the multiple exp-function method [9], which can yield three wave solutions in (3 + 1)-dimensions and resonant soliton solutions, Cole-Hopf transformation method and Bäcklund transformation method [10][11][12][13].…”

On the Solution of Nonlinear Time-Fractional Generalized Burgers Equation by Homotopy Analysis Method and Modified Trial Equation Method

“…The analytical solution of nonlinear time-fractional generalized Burgers equation by using MTEM has been obtained as following in [20]: …”

“…Gurefe has developed this approach as a Extended Trial equation method [19]. In this paper, we have modified this technique as a Modified Trial equation method (MTEM) for solving nonlinear fractional differential equations [20]- [22].…”

Infinite Sequence Solutions for Space-Time Fractional Symmetric Regularized Long Wave Equation

“…Moreover, the investigation of exact and approximate solutions for NFPDEs arising in mathematical physics, chemistry, biology, engineering, control theory, signal processing and so forth has become one of the most active and important research areas. A variety of analytical and numerical techniques have been well established and applied to solve NFPDEs, including the homogeneous balance method [6], the fractional sub-equation method [7][8][9][10][11], the exp-function method [12], the (G ′ /G)-expansion method [13,14], the first integral method [15], the modified trial equation method [16], the Jacobi elliptic equation method [17], the modified 49 Kudryashov method [18], the homotopy analysis transform method [19], the fractional variational iteration method [20], the Adomian decomposition method [21], and so on. In many analytical methods, the fractional complex transformation proposed by Li and He [22] plays a key role in converting NFPDEs into NODEs.…”