Weyl and Marchaud derivatives: a forgotten history

Abstract

In this paper we recall the contribution given by Hermann Weyl and Andr\'e Marchaud to the notion of fractional derivative. In addition we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.Comment: arXiv admin note: text overlap with arXiv:1705.00953 by other author