  In this paper, we prove the null controllability of a one-dimensional
fourth-order degenerate parabolic equation with a singular potential. Here, we
analyze cases where boundary control conditions are applied at the left
endpoint. We utilize a spectral decomposition involving Bessel functions and
their zeros in a convenient weighted Sobolev space for a degenerate parabolic
operator with specific boundary conditions. We establish the well-posedness of
the system using semigroup operator theory. Subsequently, we employ the moment
method by Fattorini and Russell to obtain an upper estimate of the cost of
controllability. Additionally, we derive a lower estimate of the cost of
controllability using a representation theorem for analytic functions of
exponential type.
