From Differences to Derivatives

Duarte Ortigueira, Manuel, and Coito, Fernando. "From Differences to Derivatives." Fractional Calculus and Applied Analysis 7.4 (2004): 459-471. <http://eudml.org/doc/11265>.

@article{DuarteOrtigueira2004,
abstract = {A relation showing that the Grünwald-Letnikov and generalized Cauchy derivatives are equal is deduced confirming the validity of a well known conjecture. Integral representations for both direct and reverse fractional differences are presented. From these the fractional derivative is readily obtained generalizing the Cauchy integral formula.},
author = {Duarte Ortigueira, Manuel, Coito, Fernando},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Fractional Difference; Grünwald-Letnikov Derivative; Generalized Cauchy Derivative; fractional difference; Grunwald-Letnikov derivative; generalized Cauchy derivative},
language = {eng},
number = {4},
pages = {459-471},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {From Differences to Derivatives},
url = {http://eudml.org/doc/11265},
volume = {7},
year = {2004},
}

TY - JOUR
AU - Duarte Ortigueira, Manuel
AU - Coito, Fernando
TI - From Differences to Derivatives
JO - Fractional Calculus and Applied Analysis
PY - 2004
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 7
IS - 4
SP - 459
EP - 471
AB - A relation showing that the Grünwald-Letnikov and generalized Cauchy derivatives are equal is deduced confirming the validity of a well known conjecture. Integral representations for both direct and reverse fractional differences are presented. From these the fractional derivative is readily obtained generalizing the Cauchy integral formula.
LA - eng
KW - Fractional Difference; Grünwald-Letnikov Derivative; Generalized Cauchy Derivative; fractional difference; Grunwald-Letnikov derivative; generalized Cauchy derivative
UR - http://eudml.org/doc/11265
ER -