On fractional derivatives of Djrbashian–Nersessian type with the nth-level Sonin kernels and their basic properties

In this paper, we introduce a concept of the nth-level general fractional derivatives that combine the Djrbashian–Nersessian fractional derivatives and the general fractional derivatives with the Sonin kernels in one definition. Then some basic properties of these fractional derivatives including the fundamental theorems of fractional calculus and a formula for their Laplace transform are presented. As an example, all results derived for the nth-level general fractional derivatives are demonstrated on the important particular case of the Djrbashian–Nersessian fractional derivative.