Solutions for Space–Time Fractional (2 + 1)-Dimensional Dispersive Long Wave Equations

First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models

“…al. presented the Conformable derivative [19,20]. Definition: If j : [0, ∞) → R is a function, then the conformable derivative of the γth order is given as,…”

“…Despite this disadvantage, it explains many properties like power rule, sequential differentiation and integration, higher order integration, property of linearity, relation between integration and differentiation, product rule, differentiation of constant function, chain rule and quotient rule [21][22][23][24]. Consequently, in solving many real world problems, researchers apply the conformable derivative, such as by obtaining the solutions to the conformable perturbed non linear Schrodinger equation [20], for the Boussinesq and combined Kdv-mKdv equation using the jacobi elliptic function expansion method [25], in solving the space-time (2+1) dimensional dispersive long wave equation [19] and in solving the conformable heat equation [26] and so forth.…”

“…For convenience, we consider a 1 (X) = 1. We inferred the deg(u(X)) can only be 0 or 1 by substituting values of a 1 (X) and r(X) in Equations (18) and (19) and balancing the degrees of the functions u(X) and a 0 (X). Let us consider u(X) = A 1 X + A 0 , therefore Equation 18takes the following form:…”

“…After substituting the values of a 0 (X), u(X) in Equation (19) and equating coefficients of the power of X, we get a nonlinear system of algebraic equations. Afterwards, we obtain different combinations of constants as given below: Case 1: we have,…”

Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system

“…In addition to these studies A. Gökdogan et al [14] gave the existence and uniqueness theorems for sequential linear conformable fractional differential equations, M. Eslami and H. Rezazadeh [11] used first integral method to give the analytical solutions of conformable fractional WuZhang system. M. Eslami [12] obtain the solitary wave solutions of space-time fractional (2 + 1)-dimensional dispersive long wave equations by using the G /G-expansion method, A. Neirameh [24] applied sub-equation method to obtain the new exact solitary wave solutions of the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity. Finally A. Atangana et al [3] presented the new properties of conformable fractional derivative.…”