Kleiner, TillmannHilfer, Rudolf2025-01-232025-01-2320221314-22241311-04541920177337http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-155743http://elib.uni-stuttgart.de/handle/11682/15574https://doi.org/10.18419/opus-15555Sequential generalized fractional Riemann-Liouville derivatives are introduced as composites of distributional derivatives on the right half axis and partially defined operators, called Dirac-function removers, that remove the component of singleton support at the origin of distributions that are of order zero on a neighborhood of the origin. The concept of Dirac-function removers allows to formulate generalized initial value problems with less restrictions on the orders and types than previous approaches to sequential fractional derivatives. The well-posedness of these initial value problems and the structure of their solutions are studied.eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/510article2024-11-02