Nonlinear dynamical analysis of drift ion acoustic shock waves in Electron-Positron-Ion plasma with adiabatic trapping

•In this paper, propagation characteristics of nonlinear coupled drift ion acoustic shock wave is investigated in an electron–positron-ion (epi) plasma in the presence of fully degenerate adiabatically trapped electrons.•A novel complex nonlinear equation with a fractional nonlinear term along with a planar dynamical system is formulated.•We then perform the nonlinear dynamical analysis of the system and presented our results in the form of time series plots and phase portraits, and corresponding shock structures.•To the best of our knowledge, for the first time, a pair of shock structures have been obtained.