论文信息 - Differences of fractional order

Differences of fractional order

Derivatives of fractional order, D af, have been considered extensively in the literature. However, little attention seems to have been given to finite differences of frac- tional order, A af. In this paper, a definition of differences of arbitrary order is presented, and A af is computed for several specific functions f (Table 2.1). We find that the operator A a 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 gen- erate series expansions involving the special functions.

J. B. Díaz | T. Osler

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