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Research Article | Open Access

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

Pshtiwan Othman Mohammed1( ), Rajendra Dahal2, Christopher S. Goodrich3, Y. S. Hamed4, Dumitru Baleanu5,6,7( )
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC 29526, United States of America
School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052, Australia
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon
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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.

Keywords

discrete fractional calculusMittag–Leffler type kernelanalytical and numerical monotonicity results
CLC number: 26A33, 26A51, 33B10, 39A12, 39B62, 65D15, 65Q20

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 5540-5550
DOI: 10.3934/math.2023279

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Cite this article:
Mohammed PO, Dahal R, Goodrich CS, et al. Analytical and numerical negative boundedness of fractional differences with Mittag–Leffler kernel. AIMS Mathematics, 2023, 8(3): 5540-5550. https://doi.org/10.3934/math.2023279

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Received: 19 October 2022
Revised: 02 December 2022
Accepted: 08 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)