The nonisospectral super integrable hierarchies associated with Lie superalgebra 𝔅(1,1)

Based on Lie superalgebra [Formula: see text], by solving the zero curvature equation of the spectral problems, we derive the nonisospectral super integrable hierarchies. Then, by adding a real number [Formula: see text], we construct the generalized Lie superalgebra [Formula: see text], and derive (1+1)-dimensional and (2+1)-dimensional nonisospectral super integrable hierarchies. Moreover, the super Hamiltonian structures of the resulting super integrable hierarchies are deduced by means of the super trace identity.