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**Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources.**
*(English)*
Zbl 1339.37051

Summary: In the paper, based on the modified Riemann-Liouville fractional derivative and Tu scheme, the fractional super NLS-MKdV hierarchy is derived, especially the self-consistent sources term is considered. Meanwhile, the generalized fractional supertrace identity is proposed, which is a beneficial supplement to the existing literature on integrable system. As an application, the super Hamiltonian structure of fractional super NLS-MKdV hierarchy is obtained.

### MSC:

37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |

35Q53 | KdV equations (Korteweg-de Vries equations) |

35R11 | Fractional partial differential equations |

17B80 | Applications of Lie algebras and superalgebras to integrable systems |

### Keywords:

generalized fractional supertrace identity; fractional super NLS-MKdV hierarchy; Hamiltonian structure; self-consistent sources
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\textit{H. H. Dong} et al., Anal. Math. Phys. 6, No. 2, 199--209 (2016; Zbl 1339.37051)

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