Differences of fractional order

Authors:
J. B. Díaz and T. J. Osler

Journal:
Math. Comp. **28** (1974), 185-202

MSC:
Primary 39A05; Secondary 26A33

DOI:
https://doi.org/10.1090/S0025-5718-1974-0346352-5

MathSciNet review:
0346352

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Abstract | References | Similar Articles | Additional Information

Abstract: Derivatives of fractional order, , have been considered extensively in the literature. However, little attention seems to have been given to finite differences of fractional order, . In this paper, a definition of differences of arbitrary order is presented, and is computed for several specific functions *f* (Table 2.1). We find that the operator 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0346352-5

Keywords:
Finite difference,
fractional differences,
fractional derivatives,
Leibniz rule,
special functions,
Mellin-Barnes contour integrals

Article copyright:
© Copyright 1974
American Mathematical Society