Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Differences of fractional order

Authors: J. B. Díaz and T. J. Osler
Journal: Math. Comp. 28 (1974), 185-202
MSC: Primary 39A05; Secondary 26A33
MathSciNet review: 0346352
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Derivatives of fractional order, $ {D^\alpha }f$, have been considered extensively in the literature. However, little attention seems to have been given to finite differences of fractional order, $ {\Delta ^\alpha }f$. In this paper, a definition of differences of arbitrary order is presented, and $ {\Delta ^\alpha }f$ is computed for several specific functions f (Table 2.1). We find that the operator $ {\Delta ^\alpha }$ is closely related to the contour integral which defines Meijer's G-function. A Leibniz rule for the fractional difference of the product of two functions is discovered and used to generate series expansions involving the special functions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 39A05, 26A33

Retrieve articles in all journals with MSC: 39A05, 26A33

Additional Information

Keywords: Finite difference, fractional differences, fractional derivatives, Leibniz rule, special functions, Mellin-Barnes contour integrals
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society