An analytical approach to obtain exact solutions of some space-time conformable fractional differential equations

Abstract In this paper, the sine-Gordon expansion method is used to obtain analytical solutions of the conformable space-time generalized reaction Duffing model and conformable space-time Eckhaus equation with the aid of symbolic computation. These equations can be reduced into ordinary differential equations (ODEs) using a suitable wave transformation with a predicted polynomial-type solution

Application of Lie Symmetry Analysis and Simplest Equation Method for Finding Exact Solutions of Boussinesq Equations

The Lie symmetry approach with simplest equation method is used to construct exact solutions of the bad Boussinesq and good Boussinesq equations. As the simplest equation, we have used the equation of Riccati

Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations

The fractional subequation method is applied to solve Cahn-Hilliard and Klein-Gordon equations of fractional order. The accuracy and efficiency of the scheme are discussed for these illustrative examples

New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations

The main purpose of this paper is to present a new approach to achieving analytical solutions of parameter containing fractional-order differential equations. Using the nonlinear self-adjoint notion, approximate solutions, conservation laws and symmetries of these equations are also obtained via a new formulation of an improved form of the Noether’s theorem. It is indicated that invariant solutions, reduced equations, perturbed or unperturbed symmetries and conservation laws can be obtained by applying a nonlinear self-adjoint notion. The method is applied to the time fractional-order Fokker–Planck equation. We obtained new results in a highly efficient and elegant manner

Exact Solutions of ϕ4 Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

This paper obtains the exact solutions of the ϕ4 equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions