Boundary value problem for the loaded equation of fractional order with forward and backward time stepping

The article considers a boundary value problem for the loaded parabolic equation involving the Riemann - Liouville derivative with forward and backward time stepping in a rectangular domain. It is proved that the problem is uniquely solvable for the class of functions satisfying the Holder condition. The issue on the solvability of the problem can be reduced to the solvability of the generalized Abel equation, and therefore to the solvability of the singular integral equation.