Abstract
In this paper, the two variables ( frac{G'}{G},frac{1}{G} ) -expansion method is applied to obtain new exact solutions with parameters of higher-dimensional nonlinear time-fractional differential equations (NTFDEs) in the sense of the conformable fractional derivative. To clarify the veracity of this method, it is implemented in nonlinear (2+1)-dimensional time-fractional biological population (BP) model and nonlinear (3+1)-dimensional KdV–Zakharov–Kuznetsov (KdV–ZK) equation with time-fractional derivative. When the parameters take some special values, the solitary and periodic solutions are obtained from the hyperbolic and trigonometric function solutions.
Highlights
Fractional differential equations (FDEs) can be viewed as the generalized type of the ordinary differential equations (ODEs)
The search for the exact solutions of FDEs plays an important role in understanding the qualitative and quantitative features of many physical phenomena, which are described by these equations
The nonlinear oscillation of an earthquake can be modeled by derivatives of fractional order
Summary
Fractional differential equations (FDEs) can be viewed as the generalized type of the ordinary differential equations (ODEs). )-expansion method is that the traveling wave solutions of nonlinear )-expansion method is that the traveling wave solutions for NTFDEs can be presented via a polynomial in the satisfies the equation )-expansion method to solve the Zakharov equations.
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