Oblique closed form solutions of some important fractional evolution equations via the modified Kudryashov method arising in physical problems

The new exact solutions for the deterministic and stochastic (2+1)-dimensional equations in natural sciences

“…Case II. When λ/((γ 2 − βλ)) < 0, substituting Equations (43)- (45) and (35) into Equations (12) and (13), we get exact travelling wave solutions of Equation (34),…”

“…Thus, many new methods have been proposed, such as the tanh-sech method [14][15][16], Jacobi elliptic function method [17][18][19], exp-function method [20,21], sine-cosine method [22][23][24], homogeneous balance method [25,26], F-expansion method [27,28], extended tanh-method [29,30], (G /G)− expansion method [31,32]. Indeed, there are recent development in analytical and numerical methods for finding solutions for NPDEs, see [33][34][35][36][37][38][39][40][41][42][43][44] and references therein.…”

Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

“…But, there are so many physical processes are still unknown to study the physical scenarios that challenged continue to determine the analytical solutions of fractional nonlinear evolution equations (FNLEEs). For this reason, scholars [22][23][24][25][26][27][28][29][30] are growing consideration to study the behavior of physical issues in science and engineering by evaluating the solutions of FNLEEs.…”

“…Conversely, references [31][32][33][34][35][36] have only constructed the analytical wave solutions of FNLEEs by overlooking obliqueness via the mathematical techniques. Very recently, a few authors [22][23][24] have only focused the influence of obliqueness on the analytical wave solutions of FNLEEs by considering the mathematical techniques, especially, the generalized exp(− φ(ξ))-expansion method and the modified Kudryashov method. They have reported that the obliqueness extensively modified the nature of wave dynamics.…”

Analytical Solutions of Nonlinear Coupled Schrodinger–KdV Equation via Advance Exponential Expansion

“…Analytical solutions allow researchers to design and perform experiments, by creating suitable natural situations, to determine these functions and parameters. There are several types of well-established methods that have been devoted to evaluate analytical solutions of NPDEs, such as the modified simple equation method [1,2], the ( / ) G G ′ expansion method [3,4], the tanh method [5,6], the Homotopy perturbation technique [7], the homogeneous balance method [8,9], the Hirota method [10], the Expfunction method [11,12], the exp ( ( )) ϕ ξ − -expansion method [13][14][15][16][17][18], the modified Kudryashov method [19], the generalized exp ( ( )) ϕ ξ − -expansion method [20,21], and so on. Due to the effectiveness of mathematical approaches, the advance exp(-( )) ξ Φ -expansion method may be easily applicable with the aid of symbolic computational software to find more general solitary and periodic wave solutions of NPDEs in mathematical physics and engineering.…”