New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method

Exact Solutions of a Family of Higher-Dimensional Space-Time Fractional KDV-Type Equations

“…Consequently, we deduce that our solutions (13), (14), (22)- (25) are new and not discussed heretofore. It is remarkable that the obtained solutions in this article have potential physical meaning for the underlying equations.…”

“…Therefore, the efficient approaches to construct the solutions of FPDEs have attracted great interest by several groups of researchers. A large collection of analytical and computational methods has been introduced for this reason, for example the exp-function method [3,4], Adomian decomposition method [5], the ( / ) G G ′ -expansion method [6], the first integral method [7,8], the variational iteration method [9], the subequation method [10,11], the modified simple equation method [12], Jacobi elliptic function expansion method [13], the generalized Kudryashov method [14,15] and so on. One of the most powerful methods for seeking analytical solutions of nonlinear differential equations is the functional variable method, which was first proposed by Zerarka et al [16,17] in 2010.…”

Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method

“…Tasbozan et al [36] solved (7) using the Jacobi elliptic function expansion method and obtained a series of exact solutions with Jacobi elliptic function forms.…”

On The Exact Solutions to Conformable Time Fractional Equations in EW Family Using Sine-Gordon Equation Approach

“…Trigonometric and hyperbolic type solutions to nonlinear PDEs can be determined by implementation of sine-cosine approach [11][12][13]. Later on, the implementations of those methods have been extended to solutions of fractional nonlinear PDEs [14][15][16][17][18][19][20][21][22][23]. Existence of some particular traveling wave transforms has given opportunity to exact solutions to fractional PDEs with nonlinear terms.…”