Analysing discrete fractional operators with exponential kernel for positivity in lower boundedness

Sarkhel Akbar Mahmood; Pshtiwan Othman Mohammed; Dumitru Baleanu; Hassen Aydi; Yasser S. Hamed; Sarkhel Akbar Mahmood; Pshtiwan Othman Mohammed; Dumitru Baleanu; Hassen Aydi; Yasser S. Hamed

doi:10.3934/math.2022579

AIMS Mathematics

2022, Volume 7, Issue 6: 10387-10399. doi: 10.3934/math.2022579

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Analysing discrete fractional operators with exponential kernel for positivity in lower boundedness

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
2.
Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey
3.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
4.
Department of Mathematics, King Abdul Aziz University, Jeddah 21577, Saudi Arabia
5.
Dniversité de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
6.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
8.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 13 February 2022 Revised: 22 March 2022 Accepted: 23 March 2022 Published: 28 March 2022
MSC : 26A48, 26A51, 33B10, 39A12, 39B62

In this paper we study the positivity analysis problems for discrete fractional operators with exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied to a discrete Caputo-Fabrizio-Caputo fractional operator of order $ \omega $ of another discrete Caputo-Fabrizio-Riemann fractional operator of order $ \beta $. Furthermore, the results are obtained for these operators with having the same orders. The conditions for the discrete fractional operators with respect to negative lower bound conditions are expressed in terms of a positive epsilon.
- discrete fractional operators,
- positivity analyses,
- exponential kernel,
- negative lower bound
Citation: Sarkhel Akbar Mahmood, Pshtiwan Othman Mohammed, Dumitru Baleanu, Hassen Aydi, Yasser S. Hamed. Analysing discrete fractional operators with exponential kernel for positivity in lower boundedness[J]. AIMS Mathematics, 2022, 7(6): 10387-10399. doi: 10.3934/math.2022579

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Abstract

In this paper we study the positivity analysis problems for discrete fractional operators with exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied to a discrete Caputo-Fabrizio-Caputo fractional operator of order $ \omega $ of another discrete Caputo-Fabrizio-Riemann fractional operator of order $ \beta $. Furthermore, the results are obtained for these operators with having the same orders. The conditions for the discrete fractional operators with respect to negative lower bound conditions are expressed in terms of a positive epsilon.

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