The Second Boundary-Value Problem in a Half-Strip for a Parabolic-Type Equation with Bessel Operator and Riemann–Liouville Partial Derivative

We study the second boundary-value problem in a half-strip for a differential equation with Bessel operator and the Riemann–Liouville partial derivative. In the case of a zero initial condition, a representation of the solution is obtained in terms of the Fox $H$-function. The uniqueness of the solution is proved for the class of functions satisfying an analog of the Tikhonov condition.