New solutions for conformable fractional Nizhnik–Novikov–Veselov system via $$G'/G$$ G ′ / G expansion method and homotopy analysis methods

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

“…Next, subrogating Eqs. (8) and (9) into Eq. (7) and setting the b j to zero, gives a nonlinear algebraic system for j = 0, 1, ..., N.…”

“…Therefore, in recent years significant efforts have been made to create analytical methods for the solution of FPDEs. These methods include the G /G expansion method for biological population models [8] and Nizhnik-Novikov-Veselov equation [9], the sine-Gordon expansion method for fractional Drinfeld-Sokolov-Wilson system [10] and Biswas-Milovic equation [11], the generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan, Ginzburg-Landau, Fokas-Lenells, Zakharov-Kuznetsov and Schrödinger equations [12][13][14][15][16][17][18][19], the first integral method for Burgers' type equations [20] and Wu-Zhang system [21] and the modified Kudryashov method for Klein-Gordon equation [22] and fractional biological population models [23], the simplest equation method for time fractional Kolmogorov-Petrovskii-Piskunov equation [24], and the Laplace and Fourier transform method for time fractional diffusion and convection-diffusion equations [25].…”

Some optical soliton solutions of space-time conformable fractional Schrödinger-type models

“…The obtained values in (19) give the following optical soliton solutions for NLS − equation, that is exact solutions for equation (14): The conformal plot of solution q 3 (x, t) with free choices of arbitrary parameters and α = 0.9 and β = 0.1 for − 0.5 t 0.5 and 0 x 10 is shown in figure 4(a). Also, figure 4(b) shows the conformal plot of solution q 3 (x, t) for α = β = 1.…”

“…f is called an α-conformable differentiable function. One may find some recent investigations on conformable fractional derivative in: Cenesiz and Kurt [17], Kurt et al [18,19], Cenesiz et al [20], Yang et al [21], Eslami et al [22], Tasbozan et al [23], Zhao and Luo [24], Zhou et al [25], Eslami et al [26]. Some useful features of the conformable fractional derivative are mentioned as follows [14,27]: Theorem 1.…”

The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta-Derivative

“…Many important techniques for analyzing exact solutions have been used in various research, including the ansatz method, modified simple equation method, extended trail equation, first integral, exp-function, and exp(-()) methods [1][2][3][4][5][6]. Some searchers have used alternative methods, such as the homotopy technique [7][8][9][10] and the extended Kudryashov method [11][12][13], modified Kudryashov and the sine-Gordon expansion approach [14][15][16][17] have also been applied by some searchers.…”