An extended Kudryashov technique for solving stochastic nonlinear models with generalized conformable derivatives

White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended G ′

“…In this paper, we constructed the white noise functional solutions of Wick-type stochastic fractional mixed KdV-mKdV equation by using the extended ðG′/GÞ-expansion method and the Hermite transform. Compared with the existing literature [5,6,8,12,13], the negative power solutions U 2 ðt, xÞ, U 4 ðt, xÞ, and U 6 ðt, xÞ obtained in the paper are not reported. The method discussed in the paper is not only applicable to Eq.…”

“…In recent years, white noise functional solution is a very important topic in the research of fractional SPDEs. Many researchers have proposed many methods to construct the white noise functional solutions of fractional SPDEs, such as the Exp-function method [5], the Kudryashov method [6], improved computational method [7], and computerized symbolic [8]. The biggest obstacle in finding the white noise functional solution of SPDE is that the nonlinear ordinary differential equation obtained by the Hermite transform and random traveling wave transform is a nonlinear ordinary differential equation with variable coefficients.…”

“…In recent years, with the development of fractional derivative, the Wick-type stochastic fractional mixed KdV-mKdV equation (see [5,6,8,12,13]), a very important class of fractional SPDE, has been widely concerned by many researchers. This model can be described as follows:…”

Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

“…Substituting (19) into Equation ( 12) and taking Equations ( 21) and ( 22) into account, yields the equality…”

“…Equation (1) has been presented in recent paper [1] as an equation whose solution can be obtained using the method of transformation for dependent and independent variables. Equation ( 1) is the generalization of some equations describing propagation pulses in the nonlinear optics (see, for example, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). The purpose of this paper is to present the method for finding solutions of Equation (1) and to obtain the implicit solitary wave solutions of Equation (1) using the transformations of variables.…”