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

doi:10.3934/math.2023279

AIMS Mathematics

2023, Volume 8, Issue 3: 5540-5550. doi: 10.3934/math.2023279

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

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
2.
Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC 29526, United States of America
3.
School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052, Australia
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
5.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
6.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
7.
Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon

Received: 19 October 2022 Revised: 02 December 2022 Accepted: 08 December 2022 Published: 19 December 2022
MSC : 26A33, 26A51, 33B10, 39A12, 39B62, 65D15, 65Q20

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.
- discrete fractional calculus,
- Mittag–Leffler type kernel,
- analytical and numerical monotonicity results
Citation: Pshtiwan Othman Mohammed, Rajendra Dahal, Christopher S. Goodrich, Y. S. Hamed, Dumitru Baleanu. Analytical and numerical negative boundedness of fractional differences with Mittag–Leffler kernel[J]. AIMS Mathematics, 2023, 8(3): 5540-5550. doi: 10.3934/math.2023279

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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.

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