Two reliable techniques for the analytical study of conformable time-fractional Phi-4 equation

Exact traveling wave solutions of the space–time fractional complex Ginzburg–Landau equation and the space-time fractional Phi-4 equation using reliable methods

“…Khan et al [36] applied the (G /G)expansion method to attain new solitary wave solutions of the space-time fractional Phi-4 equation in the sense of the modified Riemann-Liouville fractional operator. Akram [37] used the modified Kudryashov method and the exp(-Φ(ξ )) method to extract the exact solutions of the nonlinear fractional Phi-4 equation in the sense of the conformable timefractional derivative.…”

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

“…In the literature, the modified Kudryashov [19], exponential function [19], extended direct algebraic [20], mapping [21], modified mapping [21] and generalized Kudryashov [23] methods include the conformable derivatives with respect to time, while the ( ′ ⁄ , 1⁄ )expansion method [24] contains the conformable derivatives with respect to space and time. When compared with these methods, it is seen that more solutions are obtained by our method.…”

“…In recent years, searching solutions of the fractional differential equations have drawn remarkable interest not only for applied mathematicians but also for the other scientists. So far, various solutions of the time fractional Phi-four equation have been founded by utilizing the tanh function [17], modified residual power series [18], modified Kudryashov [19], exponential function [19], extended direct algebraic [20], mapping [21], modified mapping [21],homotopy analysis transform ( -HATM) [22], and generalized Kudryashov [23] methods. The solutions of space-time conformable fractional Phi-four equation is also gained by using the ( ′ ⁄ , 1⁄ )-expansion [24] method.…”

Regarding Rational Exponential and Hyperbolic Functions Solutions of Conformable Time-Fractional Phi-four Equation

“…In this section, the following form of time-fractional phi-four equation [44,45] is going to be considered for solution via exp a method. Using the transformation (4) in (1), we get (l 2 − k 2 )U + m 2 U + δU 3 = 0; δ > 0.…”

“…The Phi-four equation is a special form of the Klein-Gordon equation that prototypes the interaction of kink and anti-kink solitary waves in particle physics [43]. This paper aims to scrutinize the new explicit exact solutions for the time-fractional Phi-four equation [44,45] that may read as…”