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.
Highlights
Nonlinear fractional differential equations (FDEs) have an important role in studying various areas of engineering, physics, and applied mathematics [1,2,3,4,5]
Investigation of analytical solutions of nonlinear FDEs is very important in the analysis of some physical phenomena, such as plasma physics, solid-state physics, nonlinear optics, and so on [6
In order to understand the mechanisms of these cases, it is necessary to obtain their exact solutions [10, 11]
Summary
Nonlinear fractional differential equations (FDEs) have an important role in studying various areas of engineering, physics, and applied mathematics [1,2,3,4,5]. The following two FDEs are solved using the sine-Gordon expansion method: (I) The form of the space-time fractional Eckhaus equation iDαt φ + D2xαφ + 2Dαx |φ|2φ + |φ|4φ = 0, (1)
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