An access to fractional differentiation via fractional difference quotients

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 1975Publisher:Springer Berlin Heidelberg

Authors: Paul L. Butzer; Ursula Westphal;

doi: 10.1007/bfb0067101

An access to fractional differentiation via fractional difference quotients

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Abstract

The purpose of this paper is to introduce the fractional derivative not via fractional integration but directly as a limit of a fractional difference quotient. In the case of 2π-periodic functions this enables one to set up a fractional calculus in a norm setting with the usual rules; connections with the classical Weyl fractional derivative are given. There are applications to extensions of Hardy-Littlewood type results to the fractional situation as well as to the solution of a fractional diffusion type equation.

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