New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel
Date
2022
Authors
Mohammed, Pshtiwan Othman
Goodrich, Christopher S.
Brzo, Aram Bahroz
Baleanu, Dumitru
Hamed, Yasser S.
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Abstract
This paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The ν-monotonicity definitions, namely ν-(strictly) increasing and ν-(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with ν-monotonicity definitions, we find that the investigated discrete fractional operators will be ν2-(strictly) increasing or ν2-(strictly) decreasing in certain domains of the time scale Na := {a, a + 1, . . . }. Finally, the correctness of developed theories is verified by deriving mean value theorem in discrete fractional calculus.
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Keywords
Discrete Fractional Calculus, Monotonicity Investigations, Nabla AB-Fractional Operator
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Citation
Mohammed, Pshtiwan Othman;...et.al. "New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel", Mathematical Biosciences and Engineering, Vol.19, No.4, pp.4062-4074.
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Source
Mathematical Biosciences and Engineering
Volume
19
Issue
4
Start Page
4062
End Page
4074