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In this work, we consider Dirac-type operators with a constant delay lessthan half of the interval and not less than two-fifths of the interval. For ourconsidered Dirac-type operators, two inverse spectral problems are studied.Specifically, reconstruction of two complex $L_{2}$-potentials is studied fromcomplete spectra of two boundary value problems with one common Dirichletboundary condition and Neumann boundary condition, respectively. We giveanswers to the full range of questions usually raised in the inverse spectraltheory. That is, we give uniqueness, necessary and sufficient conditions of thesolvability, reconstruction algorithm and uniform stability for our consideredinverse problems.

Inverse problems for Dirac operators with a constant delay less than half of the interval