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Research Article | Open Access

Analysis of positivity results for discrete fractional operators by means of exponential kernels

Pshtiwan Othman Mohammed1( ), Donal O'Regan2, Aram Bahroz Brzo3, Khadijah M. Abualnaja4, Dumitru Baleanu5,6,7( )
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland
Department of Physics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
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 Mathematics, King Abdul Aziz University, Jeddah 21577, Saudi Arabia
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Abstract

In this study, we consider positivity and other related concepts such as α −convexity and α −monotonicity for discrete fractional operators with exponential kernel. Namely, we consider discrete Δ fractional operators in the Caputo sense and we apply efficient initial conditions to obtain our conclusions. Note positivity results are an important factor for obtaining the composite of double discrete fractional operators having different orders.

Keywords

discrete fractional calculusdiscrete CF-fractional operatorsmonotonicity analyses
CLC number: 26A48, 26A51, 33B10, 39A12, 39B62

References

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 15812-15823
DOI: 10.3934/math.2022865

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Cite this article:
Mohammed PO, O'Regan D, Brzo AB, et al. Analysis of positivity results for discrete fractional operators by means of exponential kernels. AIMS Mathematics, 2022, 7(9): 15812-15823. https://doi.org/10.3934/math.2022865

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Received: 02 March 2022
Revised: 22 June 2022
Accepted: 23 June 2022
Published: 15 September 2022
©2022 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)