Super integrable hierarchies associated with color Lie algebra

In this paper, by considering two non-isospectral problems with matrices chosen on the color Lie algebra ${\mathfrak{s}\mathfrak{p}}_1(6)$, we construct (1+1)-dimensional and (2+1)-dimensional super integrable systems on ${\mathfrak{s}\mathfrak{p}}_1(6)$. Moreover, based on the supertrace identity, their super Hamiltonian structures are also constructed.