Investigation of cylindrical shock waves in dusty plasma

Electronegative dusty plasma composed of Boltzmann electrons, Boltzmann negative ions, inertial positive ions and charge fluctuating dust has been considered. The fractional modified Burgers’ (FMB) equation, which is derived using Euler–Lagrange variational technique, is analytically obtained and solved for studying the cylindrical geometry effect on the propagation of the dust ion acoustic shock wave. The Laplace homotopy perturbation method, the so-called LHPM is applied to solve the FMB equation. The effect of the fractional parameter, positive ion number density at equilibrium, the number of equilibrium electrons residing on the dust grain surface and shock velocity on the behavior of the shock waves in the dusty plasma has been investigated.