Gaudin models with Uq(osp(1|2)) symmetry

We consider a Gaudin model related to the q-deformed superalgebra Uq(osp(1|2)). We present an exact solution to that system diagonalizing a complete set of commuting observables, and providing the corresponding eigenvectors and eigenvalues. The approach used in this paper is based on the coalgebra supersymmetry of the model.