Multicomponent fractional Volterra hierarchy and its subhierarchy with Virasoro symmetry

Using the Hamiltonian structures and tau symmetries, we construct a multicomponent fractional Volterra hierarchy (MFVH) as an example of a generalized integrable system. We study the Hirota bilinear equation and the Virasoro symmetry for this hierarchy. As a reduction of the MFVH from a commutative subalgebra, we construct the fractional $Z_N$-Volterra hierarchy and its Virasoro symmetry.