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A fractional quadratic-form identity is derived from a general isospectral problem of fractional order, which is devoted to constructing the Hamiltonian structure of an integrable coupling of the fractional BK hierarchy. The method can be generalized to other fractional integrable couplings

The Fractional Quadratic-Form Identity and Hamiltonian Structure of an Integrable Coupling of the Fractional Broer-Kaup Hierarchy