Numerical solution and characteristic study of time-fractional shocks collision

Abstract

In this study, the interaction of counter-propagating ion acoustic shock waves in three-component unmagnetized plasmas with inertial warm ions, superthermal electrons and positrons are examined. By employing the extended Poincare-Lighthill-Kuo (PLK) method, two-sided Korteweg-deVries-Burgers (KdVB) equations and their corresponding phase shifts for the shock wave are also derived. The derived two-sided KdVB equations are converted to two-sided time-fractional KdVB (TFKdVB) equations by semi inverse method, which is then solved numerically by a local meshless method (LMM). The effects of the ratio of electron temperature to positron temperature, the spectral index and fractional concentration of positron component p on the phase shift are also examined. Figures are given to judge the performance of the LMM. Comparison is made with the exact solution for the classical case (i.e. ρ = 1) and with Petrov-Galerkin method (PGM) in case of fractional derivative. The influence of the fractional parameter on the behaviour of ion acoustic shock wave in e-p-i plasma is investigated.