New Analytical Solutions for Space and Time Fractional Phi-4 Equation

Abstract

In this paper, the largest set in the literature of space, time and space-time conformable fractional Phi-4 equations is found by utilizing an analytical method based upon the Jacobi elliptic functions. These solutions are obtained in a general form including trigonometric, rational, complex and hyperbolic functions. Some problems are presented to illustrate the practical application of the proposed method and some of the solutions are also demonstrated with the two-dimensional and three-dimensional graphics.

Solitary and Periodic Wave Solutions of the Space-Time Fractional Extended Kawahara Equation

“…Literally, in the Jacobi elliptic function (JEF) expansion method, the solutions of the given problems are investigated in terms of these functions. The JEF expansion method has been used several times to attain solutions for multifarious classes of equations either of the integer order or the fractional order [13,26,31,[41][42][43][44]. In the solution process, before applying the mentioned expansion method, the fractional extended Kawahara equation is transformed into an integer order ordinary differential equation in a new variable by using a suitable transformation to change the variables.…”

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

“…Some of them are seen in Ref. [32][33][34][35][36]. The Jacobi elliptic function solutions of Eq.…”

Exact solutions of time fractional Korteweg–de Vries–Zakharov–Kuznetsov equation

“…The analytic method for this equation is not yet available in the literature. On the other side, in order to gain the exact solutions of different conformable fractional partial differential equations, Jacobi elliptic functions have been utilized in pervious works 17–20 . For the suggested method, the derivative using in Equation does not need to be conformable.…”