In this manuscript, we study the parameter-dependent conformable Sturm–Liouville problem (PDCSLP) in which its transmission conditions are arbitrary finite numbers at an interior point in [0, π]. Also, we prove the uniqueness theorems for inverse second order of conformable differential operators by applying three spectra with jumps and eigen-parameter-dependent boundary conditions. To this end, we investigate the PDCSLP in three intervals [0, π], [0, p], and [p, π] where p ∈ (0, π) is an interior point.
