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

Abstract

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.

Keywords

• discrete fractional calculus
• mittag–leffler type kernel
• analytical and numerical monotonicity results