In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations.
We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. Based on this formulation, a solitary solution can be easily obtained using the Ritz method. The Kudryashov method is used to construct exact solutions of the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system.
Moreover, it is observed that the suggested techniques are compatible with the physical nature of such problems.
Akbari, M., & Taghizadeh, N. (2015). Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations. Caspian Journal of Mathematical Sciences, 4(2), 215-225.
MLA
M. Akbari; N. Taghizadeh. "Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations", Caspian Journal of Mathematical Sciences, 4, 2, 2015, 215-225.
HARVARD
Akbari, M., Taghizadeh, N. (2015). 'Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations', Caspian Journal of Mathematical Sciences, 4(2), pp. 215-225.
VANCOUVER
Akbari, M., Taghizadeh, N. Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations. Caspian Journal of Mathematical Sciences, 2015; 4(2): 215-225.
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