  In this paper, we first deal with the general fractional derivatives of
arbitrary order defined in the Riemann-Liouville sense. In particular, we
deduce an explicit form of their null space and prove the second fundamental
theorem of Fractional Calculus that leads to a closed form formula for their
projector operator. These results allow us to formulate the natural initial
conditions for the fractional differential equations with the general
fractional derivatives of arbitrary order in the Riemann-Liouville sense. In
the second part of the paper, we develop an operational calculus of the
Mikusi\'nski type for the general fractional derivatives of arbitrary order in
the Riemann-Liouville sense and apply it for derivation of an explicit form of
solutions to the Cauchy problems for the single- and multi-term linear
fractional differential equations with these derivatives. The solutions are
provided in form of the convolution series generated by the kernels of the
corresponding general fractional integrals.
