Analytic wave solutions of beta space fractional Burgers equation to study the interactions of multi-shocks in thin viscoelastic tube filled

Abstract

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.

Keywords

• Beta fractional derivative
• Burgers equation
• Multi-shocks
• Viscoelastic tube filled