Second boundary-value problem in a half-strip for equation of parabolic type with the Bessel operator and Riemann–Liouville derivative

We investigate the second boundary-value problem in the half-strip for parabolic equation with the Bessel operator and Riemann–Liouville partial derivative. In terms of the integral transform with Wright function in the kernel, we find the representation of a solution in the case of zero edge condition. We prove the uniqueness of a solution in the class of functions satisfying an analog of the Tikhonov condition.