๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A Correction to Leibniz Rule for Fractional Derivatives

โœ Scribed by Osler, Thomas J.

Book ID
118202198
Publisher
Society for Industrial and Applied Mathematics
Year
1973
Tongue
English
Weight
282 KB
Volume
4
Category
Article
ISSN
0036-1410

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper calls attention to an error in the proofs of various extensions of the "Leibniz rule" for the fractional derivative of the product of two functions published previously by the author. The error occurs at a step where integration and summation must be interchanged, and justified. The justification requires that a new restriction be added to the functions involved. The new restriction, however, is a natural one, and in no way affects applications of the Leibniz rule previously published.

๐Ÿ“œ SIMILAR VOLUMES

The fractional correction rule: a new pe
The fractional correction rule: a new perspective
โœ Mitra Basu; Quan Liang ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 372 KB

In this paper we discover and explore a useful property of the fractional correction rule, a variation of the perceptron learning rule, for a single neural unit. We rename this rule the projection learning rule (PrLR), which seems more appropriate because of the technique that we use to prove conver

Quadrature rule for Abelโ€™s equations: Un
Quadrature rule for Abelโ€™s equations: Uniformly approximating fractional derivatives
โœ Hiroshi Sugiura; Takemitsu Hasegawa ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 514 KB

An automatic quadrature method is presented for approximating fractional derivative D q f (x) of a given function f (x), which is defined by an indefinite integral involving f (x). The present method interpolates f (x) in terms of the Chebyshev polynomials in the range [0, 1] to approximate the frac

The integral analogue of the Leibniz rul
The integral analogue of the Leibniz rule for fractional calculus and its applications involving functions of several variables
โœ B.B. Jaimini; N. Shrivastava; H.M. Srivastava ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 424 KB

The authors apply certain operators of fractional calculus (that is, integrals and derivatives of arbitrary real or complex order) with a view to evaluating various families of infinite integrals associated with functions of several variables. They also present relevant connections of the infinite i