The use of improved generalized Riccati equation mapping method has been demonstrated to find some new exact travelling wave solutions to space-time fractional non-liner double dispersive equation (DDE). The equation is used for modelling wave propagation in elastic inhomogeneous Murnaghan's rod. We have used Caputo's fractional derivative to achieve the fractional version of Murnaghan's rod equation. Improved generalized Riccati equation mapping method proves to be very effective tool to find a variety of soliton solutions. As a result, we found many new and general solutions including dark, combined dark-bright, singular periodic wave, combined singular periodic wave solutions and rational solutions. We have simulated the solitons, to check their types, with the help of graphs and all the solutions obtained in this article have been verified by back substitution in original equation by using Maple 17.

已经证明，使用改进的广义Riccati方程映射方法可以找到时空分数非线性双色散方程（DDE）的一些新的精确行波解。该方程用于对弹性非均质Murnaghan杆中的波传播进行建模。我们已经使用Caputo的分数导数来获得Murnaghan杆方程的分数形式。改进的广义Riccati方程映射方法被证明是找到各种孤子解的非常有效的工具。结果，我们发现了许多新的通用解决方案，包括暗，暗-暗组合，奇异周期波，组合奇异周期波解决方案和有理解。我们已经模拟了孤子，以检查它们的类型，