A comparative study on overtaking collisional ion-acoustic multi-soliton around the critical values in the sense of fractal and fractional differential operators

The time–space fractional modified Korteweg de-Vries (TSF-mKdV) equation is considered to investigate the nonlinear overtaking ion-acoustic multi-solitons around the critical values of any specific physical parameter in an unmagnetized collisionless plasma. To do so, various fractional derivative operators are considered. The TSF-mKdV equation is actually obtained by applying the Agrawal technique to the typical mKdV equation. The Hirota’s direct bilinear approach is used to obtain the proposed multi-soliton solutions to the TSF-mKdV model equation. In the framework under study, the effects of the space–time fractional parameters and plasma parameters on the overtaking collision of multi-soliton wave propagation are examined.