Numerical Investigation of Nonlinear Shock Wave Equations with Fractional Order in Propagating Disturbance

The symmetry design of the system contains integer partial differential equations and fractional-order partial differential equations with fractional derivative. In this paper, we develop a scheme to examine fractional-order shock wave equations and wave equations occurring in the motion of gases in the Caputo sense. This scheme is formulated using the Mohand transform (MT) and the homotopy perturbation method (HPM), altogether called Mohand homotopy perturbation transform (MHPT). Our main finding in this paper is the handling of the recurrence relation that produces the series solutions after only a few iterations. This approach presents the approximate and precise solutions in the form of convergent results with certain countable elements, without any discretization or slight perturbation theory. The numerical findings and solution graphs attained using the MHPT confirm that this approach is significant and reliable.

Automated summary

In this paper, a scheme using the Mohand transform and the homotopy perturbation method is developed to handle fractional-order shock wave equations and wave equations. The approach allows for obtaining series solutions from the recurrence relation after only a few iterations and presents approximate and precise solutions in the form of convergent results.