  In this paper, we first provide a short summary of the main properties of the
so-called general fractional derivatives with the Sonin kernels introduced so
far. These are integro-differential operators defined as compositions of the
first order derivative and an integral operator of convolution type. Depending
on succession of these operators, the general fractional derivatives of the
Riemann-Liouville and of the Caputo types were defined and studied. The main
objective of this paper is a construction of the 1st level general fractional
derivatives that comprise both the general fractional derivative of the
Riemann-Liouville type and the general fractional derivative of the Caputo
type. We also provide some of their properties including the 1st and the 2nd
fundamental theorems of Fractional Calculus for these derivatives and the
suitably defined general fractional integrals.
