Boundary controllability for a 1D degenerate parabolic equation with drift and a singular potential

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and singular potential. study case when potential arises at left endpoint weighted Dirichlet boundary control is located this point. get spectral decomposition suitable operator, defined in Sobolev space, involving Bessel functions their zeros, then we use moment method by Fattorini Russell to obtain an upper estimate cost controllability. also lower using representation theorem for analytic exponential type.