In this paper, a class of super Heisenberg-Virasoro algebras is introduced on the base of conformal modules of Lie conformal superalgebras. Then we construct a class of simple super Heisenberg-Virasoro modules, which is induced from simple modules of the finite-dimensional solvable Lie superalgebras. These modules are isomorphic to simple restricted super Heisenberg-Virasoro modules, and include the highest weight modules, Whittaker modules and high order Whittaker modules.
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