Year: 2019
Author: Jinfa Cheng
Journal of Mathematical Study, Vol. 52 (2019), Iss. 1 : pp. 38–52
Abstract
In this paper, a generalized multivariate fractional Taylor's and Cauchy's mean value theorem of the kind
f(x,y)=n∑j=0Djαf(x0,y0)Γ(jα+1)+Rαn(ξ,η),f(x,y)−n∑j=0Djαf(x0,y0)Γ(jα+1)g(x,y)−n∑j=0Djαg(x0,y0)Γ(jα+1)=Rαn(ξ,η)Tαn(ξ,η),
where 0<α≤1, is established. Such expression is precisely the classical Taylor's and Cauchy's mean value theorem in the particular case α=1. In addition, detailed expressions for Rαn(ξ,η) and Tαn(ξ,η) involving the sequential Caputo fractional derivative are also given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v52n1.19.04
Journal of Mathematical Study, Vol. 52 (2019), Iss. 1 : pp. 38–52
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Sequential Caputo fractional derivative generalized Taylor's mean value theorem generalized Taylor's formula generalized Cauchy' mean value theorem generalized Cauchy's formula.
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