New complex wave structures to the complex Ginzburg-Landau model

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

“…In this subsection, the generalized Kudryashov procedure will be applied to the equation (16). According to the method, we assume…”

“…In literature, lots of researchers obtained the exact solutions of the given model with the diferent types of nonlinearity. Some researchers obtained the exact solutions of the generalized derivative of the given model for example Kudryashov applied the frst integral method to the equation in [14], Das et al applied the F-expansion to the model in [15], the modifed (G ′ /G)-expansion method is applied to the model by Wang et al in [16], the modifed Jacobi elliptic expansion method is applied by Hosseini et al in [17], Hosseini et al implemented Kudryashov and exponential methods to the model including the parabolic nonlinearity in [18]. Some researchers obtained the exact solutions of equation ( 1) with diferent kinds of fractional derivatives, for example, Tozar obtained the analytical solutions of the conformable time-fractional complex Ginzburg-Landau equation with the help of the (1/G ′ ) method in [19], optical solutions were discovered with the help of the generalized exponential rational function method in [20], Sulaiman et al explored the optical solitons with the help of the extended sinh-Gordon equation expansion method in [21], the form of the space-time conformable fractional complex Ginzburg-Landau equation is handled in [22], Sadaf et al applied the (w(ξ)/2) method to the model with the diferent types of senses as the conformable, beta, truncated derivatives in [23].…”

Discovering the innumerable solutions of the (1 +1 ) -dimensional integro-differential Ito and (2 + 1 ) -dimensional integro-differential Sawda-Kotera equations via an efficient analytical technique

“…Equation with Conformable Derivative Dependent on Time Parameter to find the Exact Dynamic Wave Solutions. The others feasible methods are the generalized Kudryashov method [36], the modified (𝐺 ′ 𝐺 ⁄ )-expansion method [37], the integration method [38], the modified symbolic computation method [39], the Hirota's bilinear operator's method [40], the tanh-function method [41]. Several researchers used the above mentioned (𝐺′ 𝐺 ⁄ )-expansion method to explore exact solution of different type of NLPDEs.…”