The fractional supertrace identity and its application to the super Jaulent–Miodek hierarchy

In this paper, a fractional supertrace identity on superalgebras and Hamiltonian structure of the fractional soliton equation hierarchy are presented by using the modified Riemann–Liouville derivative and exterior derivatives of fractional orders. As applications, we get the fractional super Jaulent–Miodek (JM) hierarchy and its super Hamiltonian structure by using fractional supertrace identity. This method can be used to get more fractional super hierarchies.

► A fractional supertrace identity was proposed for the first time.
► Hamiltonian structure of the fractional super soliton equation hierarchy.
► The fractional super JM hierarchy are presented.
► The super Hamiltonian structure of JM hierarchy are presented by using of fractional supertrace identity.