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

doi:10.3934/math.2022579

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 ω of another discrete Caputo-Fabrizio-Riemann fractional operator of order β. 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.

Original language	English
Pages (from-to)	10387-10399
Number of pages	13
Journal	AIMS Mathematics
Volume	7
Issue number	6
DOIs	https://doi.org/10.3934/math.2022579
Publication status	Published - 2022
Externally published	Yes

Keywords

discrete fractional operators
exponential kernel
negative lower bound
positivity analyses

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10.3934/math.2022579

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title = "Analysing discrete fractional operators with exponential kernel for positivity in lower boundedness",

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 ω of another discrete Caputo-Fabrizio-Riemann fractional operator of order β. 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.",

keywords = "discrete fractional operators, exponential kernel, negative lower bound, positivity analyses",

author = "Mahmood, {Sarkhel Akbar} and Mohammed, {Pshtiwan Othman} and Dumitru Baleanu and Hassen Aydi and Hamed, {Yasser S.}",

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AU - Mahmood, Sarkhel Akbar

AU - Mohammed, Pshtiwan Othman

AU - Baleanu, Dumitru

AU - Aydi, Hassen

AU - Hamed, Yasser S.

PY - 2022

Y1 - 2022

N2 - 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 ω of another discrete Caputo-Fabrizio-Riemann fractional operator of order β. 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.

AB - 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 ω of another discrete Caputo-Fabrizio-Riemann fractional operator of order β. 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.

KW - discrete fractional operators

KW - exponential kernel

KW - negative lower bound

KW - positivity analyses

UR - http://www.scopus.com/inward/record.url?scp=85127019344&partnerID=8YFLogxK

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DO - 10.3934/math.2022579

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SP - 10387

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JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 6

ER -

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

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