Abstract
In this paper, we get many new analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov Kuznetsov (mKDV-ZK) equation by means of a new approach namely method of undetermined coefficients based on a fractional complex transform. These solutions have physics meanings in natural sciences. This method can be used to other nonlinear fractional differential equations.
Highlights
Nonlinear fractional differential equations (NFDEs) are universal models of the classical differential equations of integer order
We get many new analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov Kuznetsov equation by means of a new approach namely method of undetermined coefficients based on a fractional complex transform
These solutions have physics meanings in natural sciences. This method can be used to other nonlinear fractional differential equations
Summary
Nonlinear fractional differential equations (NFDEs) are universal models of the classical differential equations of integer order. The fractional order derivative and integral is becoming a hot spot of international research; it can more accurately describe the nonlinear phenomena in physics. Such as chemical kinematics, chemical physics and geochemistry, communication, physics, biology, engineering, mathematics, diffusion processes in porous media, in vibrations in a nonlinear string, power-law non-locality, and power-law longterm memory can use NFDEs as models to express these problem [1] [2] [3] [4] [5].
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