The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann–Liouville partial derivative

The paper is devoted to the first boundary-value problem in a rectangular domain for a differential equation with the singular Bessel operator acting with respect to a spatial variable and the Riemann–Liouville fractional differentiation operator acting with respect to a time variable. An explicit representation of the solution is constructed. The uniqueness of the solution is proved in the class of functions satisfying the Hölder condition with respect to the time variable. When the order of the fractional derivative is equal to unity, and the Bessel operator has no singularity, the studied equation coincides with the heat equation and the obtained results coincide with well-known corresponding classical results.