Open AccessAnalysis of discrete fractional operators
Author(s) -
Ferhan M. Atıcı,
Meltem Uyanik
Publication year - 2015
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm150218007a
Subject(s) - monotonic function , mathematics , fractional calculus , sign (mathematics) , operator (biology) , function (biology) , domain (mathematical analysis) , pure mathematics , discrete mathematics , calculus (dental) , mathematical analysis , medicine , biochemistry , chemistry , dentistry , repressor , evolutionary biology , biology , transcription factor , gene
In this paper, we introduce two new monotonicity concepts for a nonnegative or nonpositive valued function defined on a discrete domain. We give examples to illustrate connections between these new monotonicity concepts and the traditional ones. We then prove some monotonicity criteria based on the sign of the fractional difference operator of a function f, ??f with 0 < ? < 1. As an application, we state and prove the mean value theorem on discrete fractional calculus.