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Browsing by Author "Goodrich, Christopher S."

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    Analytical and numerical negative boundedness of fractional differences with Mittag-Leffler kernel
    (2023) Baleanu, Dumitru; Dahal, Rajendra; Goodrich, Christopher S.; Hamed, Y. S; Baleanu, Dumitru; 56389
    We show that a class of fractional differences with Mittag-Leffler kernel can be negative and yet monotonicity information can still be deduced. Our results are complemented by numerical approximations. This adds to a growing body of literature illustrating that the sign of a fractional difference has a very complicated and subtle relationship to the underlying behavior of the function on which the fractional difference acts, regardless of the particular kernel used.
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    Article
    New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel
    (2022) Baleanu, Dumitru; Goodrich, Christopher S.; Brzo, Aram Bahroz; Baleanu, Dumitru; Hamed, Yasser S.; 56389
    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.