Compositions of fractional derivatives as Dzhrbashyan — Nersesyan derivative

The issues of unique solvability for a special initial value problem to two classes of a linear inhomogeneous equation with a derivative of Dzhrbashyan — Nersesyan are investigated. In one of the classes, the operator at the unknown function is bounded, in the other it is sectorial. The representation of the composition of any number of Gerasimov — Caputo and/or Riemann — Liouville differential operators in the form of a Dzhrbashyan — Nersesyan derivative is also proved.