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

Pshtiwan Othman Mohammed; Donal O'Regan; Aram Bahroz Brzo; Khadijah M. Abualnaja; Dumitru Baleanu; Pshtiwan Othman Mohammed; Donal O'Regan; Aram Bahroz Brzo; Khadijah M. Abualnaja; Dumitru Baleanu

doi:10.3934/math.2022865

AIMS Mathematics

2022, Volume 7, Issue 9: 15812-15823. doi: 10.3934/math.2022865

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

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
2.
School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland
3.
Department of Physics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
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 Mathematics, King Abdul Aziz University, Jeddah 21577, Saudi Arabia

Received: 02 March 2022 Revised: 22 June 2022 Accepted: 23 June 2022 Published: 27 June 2022
MSC : 26A48, 26A51, 33B10, 39A12, 39B62

In this study, we consider positivity and other related concepts such as $ \alpha- $convexity and $ \alpha- $monotonicity for discrete fractional operators with exponential kernel. Namely, we consider discrete $ \Delta $ 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.
- discrete fractional calculus,
- discrete CF-fractional operators,
- monotonicity analyses
Citation: Pshtiwan Othman Mohammed, Donal O'Regan, Aram Bahroz Brzo, Khadijah M. Abualnaja, Dumitru Baleanu. Analysis of positivity results for discrete fractional operators by means of exponential kernels[J]. AIMS Mathematics, 2022, 7(9): 15812-15823. doi: 10.3934/math.2022865

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Abstract

In this study, we consider positivity and other related concepts such as $ \alpha- $convexity and $ \alpha- $monotonicity for discrete fractional operators with exponential kernel. Namely, we consider discrete $ \Delta $ 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.

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