The present work investigates the single and overtaking collision of multi-shock wave excitations having space fractional evolution in a thin viscoelastic tube filled with incompressible inviscid fluid. The previously proposed model equations are considered to study such physical scenarios. The spatial fractional Burgers equation is formulated by implementing the reductive perturbation method form the considered model equations. The new analytical solutions for single and overtaking collision of multi-shocks are constructed by implementing the rational exponential functions directly. With the changes of physical parameters, the behaviors of single and overtaking collision of multi-shocks are displayed graphically and described physically. It is found that the overtaking collisions of multi–shocks are produced with the presence of beta nonlocal operator. The single and interactions of multi-shocks are also significantly changed with the change of physical parameters. The obtained results are very useful in describing the nature of overtaking collision of multi-shocks in various environments, particularly in large blood vessels and further laboratory studies.

本工作研究在充满不可压缩的粘性流体的细粘弹性管中具有空间分数演化的多冲击波激发的单次和超车碰撞。考虑使用先前提出的模型方程式来研究此类物理场景。通过实施归纳摄动法，从考虑的模型方程式中得出空间分数Burgers方程。通过直接实现有理指数函数，构造了多冲击单次和超车碰撞的新解析解。随着物理参数的变化，以图形方式显示并描述了多冲击的单次和超车碰撞行为。发现存在β非本地算子时会产生多震荡的超车碰撞。多次冲击的单次和相互作用也随着物理参数的变化而显着变化。获得的结果对于描述在各种环境中，特别是在大血管中以及进一步的实验室研究中，多冲击的超车碰撞的性质非常有用。