AIMS Mathematics (Jan 2023)

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

  • Pshtiwan Othman Mohammed ,
  • Rajendra Dahal,
  • Christopher S. Goodrich,
  • Y. S. Hamed,
  • Dumitru Baleanu

DOI
https://doi.org/10.3934/math.2023279
Journal volume & issue
Vol. 8, no. 3
pp. 5540 – 5550

Abstract

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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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