An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

•We study fractional modified Degasperis-Procesi equation.•The fractional arises in Propagation of Nonlinear Dispersive Waves.•The q-HASTM is applied to obtain the solution of the problem.•The impact of order of fractional derivative is demonstrated graphically.