Constructions of the optical solitons and other solitons to the conformable fractional Zakharov–Kuznetsov equation with power law nonlinearity

The current research manifests kink wave answers, mixed singular optical solitons, the mixed dark-bright lump answer, the mixed dark-bright periodic wave answer, and periodic wave answers to the conformable fractional ZK model, including power law nonlinearity by plugging the revised -expansion process. The constraint requirements for the occurrence of substantial solitons are provided. Under the selection of proper values of a, b, n, t, λ, μ and α, the 2D and 3D pictures to a few of the recorded answers are sketched. From our obtained solutions, we might decide that the investigated procedure is hugely muscular, sincere, and essential in rendering various new soliton solutions of distinct nonlinear conformable fractional evolution equations and accordingly, we shall bring it up in our future investigations.

In this paper, the modified (G /G)-expansion process will obtain soliton answers of the following conformable fractional ZK model, including power law nonlinearity [28,46]. We are considering that using above model [28,46], is the nonlinearity and ∂ ∂x ∂ 2 u ∂x 2 + ∂ 2 u ∂y 2 + ∂ 2 u ∂z 2 is dispersion. Solitons are the outcome of a rule between dispersion and nonlinearity. The above model typically appears in the analysis of plasma physics. Matebese et al. [46] noted the above model through the three analytical methods, such as the (G /G)-expansion method, the extended tanh function method, and the ansatz method. Besides, Aminikhah et al. [47] attempted to discover the same model when α = 1 plugging the functional variable method. The particular case where n = 1 and α = 1 provides the (3 + 1)-dimensional Zakharov-Kuznetsov equation. Section 2 provides a few fundamental aspects and the knowledge of the conformable fractional calculus theory. The novel closedform wave answers of the recommended model are discussed in Section 4. The last section conveys the conclusions and future tasks.
for all t > 0, α ∈ (0, 1). If f is α-differentiable in some (0, a), a > 0 and lim t→0 + ( t D α f (t)) exists, then in accordance with the definition, we obtain The novel definition convinces the characteristics manifested in the following theorem.

Theorem 2.2:
We consider that α ∈ (0, 1], and f, g be αdifferentiable at a point t, such that [50] established the chain rule under the conformable fractional derivatives.

Theorem 2.3:
We consider that f : (0, ∞) → R is a function, for example, f is differentiable and also α-differentiable. Let us consider that g is a function defined in the range of f and also differentiable. Then one has the following rule:

The fractional complex transformation
This section implements the complex fractional transformation for the fractional-order PDE: where L = u(x, y, t). For Equation (5) where V stands for the travelling wave speed. Then, Equation (5) becomes
Plugging Equation (12) into Equation (11) and then calculating each coefficients of F i (±1, ±2, . . . . . . ., ±m) to zeros, we obtain the following relations: and use the values of the Phase 1 into Equation (12), we obtain: and plug the values of the Phase 2 into Equation (12), we get: an A −1 = 0, and A −2 = 0 and plug the values of the Phase 3 into Equation (12), we obtain:      − 3b(λ 2 n − 4μn + n − 1) an , A −1 = 0, and 8an . Similarly, we can provide new five soliton answers to the case mentioned above of the studied model, which are omitted for assistance. • Phase 5: Similarly, we can provide new five soliton answers to the case mentioned above of the studied model, which are omitted for assistance. . Similarly, we can provide new five soliton answers to the case mentioned above of the studied model, which are omitted for assistance.
A graphical description is an essential tool for analysis and to communicate the answers to the problems lucidly. When working the calculation in daily life, we require the fundamental knowledge of securing the use of graphs. Hence, the graphical displays of some of the obtained solutions are demonstrated in Figures 1-6.

Conclusions and future work
We have examined the modified (G /G)-expansion process for generating closed-form wave answers of the conformable fractional ZK equation, including power law nonlinearity. This scheme permits us to establish more many nonlinear conformable fractional evolution models in mathematical sciences by the examined models. As a consequence, various new types of closed-form wave answers are achieved. From our expert answers, we strongly conclude that the studied idea is great brawny, reliable, and crucial in executing numerous new closed-form wave answers of different nonlinear conformable FDEs. Finally, we mention that the process can be made to various distinct nonlinear conformable FDEs that occur in the area of mathematical physics.