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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Butzer, P.L., Westphal, U. (1975). An access to fractional differentiation via fractional difference quotients. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067101
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DOI: https://doi.org/10.1007/BFb0067101
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