Analytical and numerical negative boundedness of fractional differences with Mittag–Leffler kernel

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 h...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 3; pp. 5540 - 5550
Main Authors Mohammed, Pshtiwan Othman, Dahal, Rajendra, Goodrich, Christopher S., Hamed, Y. S., Baleanu, Dumitru
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
analytical and numerical monotonicity results
discrete fractional calculus
mittag–leffler type kernel
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023279