Abstract The wave propagation in micro structured solids is described by conformable time fractional strain wave equation and should be able to account for several scales of micro-structure. ( G ′ G 2 ) -expansion method has been used to propagate the different types of solutions like hyperbolic functions, trigonometric functions and rational functional solutions. All the solutions are listed with their existence criterion on the parameters. A sufficient condition for the convergence of ( G ′ G 2 ) -expansion method is provided. Meantime, considered equation is transformed into planar dynamical system after using traveling wave transfiguration. Then quasiperiodic behavior is investigated for the discussed model for different values of the physical parameters ( α , ϖ , ζ , V and β) after applying a periodic external force. Further, to strengthen the claimed results sensitive analysis is used for different initial value problems.

中文翻译：

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具有适形时间分数应变波动方程的微结构固体动力学行为

摘要 波在微结构固体中的传播是由一致的时间分数应变波动方程描述的，应该能够考虑到微观结构的几个尺度。( G ′ G 2 ) -展开方法已被用于传播不同类型的解，如双曲函数、三角函数和有理泛函解。所有的解都列出了它们在参数上的存在准则。给出了( G ′ G 2 )-展开法收敛的充分条件。同时，利用行波变换将所考虑的方程转化为平面动力系统。然后，在施加周期性外力后，针对物理参数（α、ϖ、ζ、V 和 β）的不同值，研究了所讨论模型的准周期行为。更多，