Abstract
In this work, we present \(\left (G^{\prime }/G, 1/G\right )\)-expansion method for solving fractional differential equations based on a fractional complex transform. We apply this method for solving space–time fractional Cahn–Allen equation and space–time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann–Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced. The obtained solutions may be used for explaining of some physical problems. The \( \left (G^{\prime }/G, 1/G\right )\)-expansion method has a wider applicability for nonlinear equations. We have verified all the obtained solutions with the aid of Maple.
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YAŞAR, E., GIRESUNLU, İ.B. The \(\boldsymbol {\left (G^{\prime }/G,1/G\right )}\)-expansion method for solving nonlinear space–time fractional differential equations. Pramana - J Phys 87, 17 (2016). https://doi.org/10.1007/s12043-016-1225-7
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DOI: https://doi.org/10.1007/s12043-016-1225-7
Keywords
- Exact solution
- modified Riemann–Liouville fractional derivative
- space–time Cahn–Allen equation; space–time Klein–Gordon equation
- \(\left (G^{\prime }/G, \protect 1/G\right ) \)-expansion method