T. Kleiner, R. Hilfer
Fractional Calculus and Applied Analysis 25, 267-298 (2022)
https://doi.org/10.1007/s13540-021-00012-0
submitted on
Friday, October 15, 2021
Sequential 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.
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