On the 1st-Level General Fractional Derivatives of Arbitrary Order

In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for first time. We start with a generalization Sonin condition kernels integrals then specify set that satisfy possess an integrable singularity power law type at origin. The integro-differential operators convolution from set. They contain both Riemann–Liouville regularized considered in literature so far. For order, some important properties, including 1st 2nd fundamental theorems calculus, formulated proved.