Fig. 4

Time evolutionary process depicted for the discrete fractional-order MPXV model (3.3) with respect to \(\wp =1\) and \(\wp =[0.95 ~0.9~0.85~0.75]\) for paring up (a,b) \(\textrm{X}_{\hbar }\) and \(\textrm{R}_{\hbar },\) (c,d) \(\textrm{X}_{\hbar }\) and \(\mathcal {I}_{\mathcal {A}},\) and (g-i) \(\textrm{Y}_{\hbar }\) and \(\mathcal {I}_{\mathcal {B}},\) respectively.