Analysis of a basic SEIRA model with Atangana-Baleanu derivative

Sümeyra Uçar; Sümeyra Uçar

doi:10.3934/math.2020097

AIMS Mathematics

2020, Volume 5, Issue 2: 1411-1424. doi: 10.3934/math.2020097

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Research article

Analysis of a basic SEIRA model with Atangana-Baleanu derivative

Sümeyra Uçar ^,

Department of Mathematics, Balıkesir University, Turkey

Received: 23 October 2019 Accepted: 09 January 2020 Published: 20 January 2020
MSC : 34A08, 34A34, 47H10

Since computer worms have very acute and negative effects on computer systems, they are considered as one of the malicious bodies that induce serious issues in these structures. This is why numerous efforts have been given for finding different ways to avert the unwanted occurrences which stem from computer worms' harmful behavior to this day. Our motivation is to make use of AtanganaBaleanu fractional derivative with Mittag-Leffler kernel which has latterly been brought into operation, and thus closely examine the basic SEIRA (susceptible-exposed-infectious-removed-antidotal) model associated with computer worms. To that end, we first prove the conditions that show the existence and uniqueness properties of the solutions for the fractional order model benefiting from fixed point theory. By using various values belonging to the fractional order, we also acquired different numerical simulations emphasizing that the aforementioned derivative is quite impactful.
- Atangana-Baleanu derivative,
- fixed point theory,
- existence,
- uniqueness,
- mathematical model
Citation: Sümeyra Uçar. Analysis of a basic SEIRA model with Atangana-Baleanu derivative[J]. AIMS Mathematics, 2020, 5(2): 1411-1424. doi: 10.3934/math.2020097

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Abstract

Since computer worms have very acute and negative effects on computer systems, they are considered as one of the malicious bodies that induce serious issues in these structures. This is why numerous efforts have been given for finding different ways to avert the unwanted occurrences which stem from computer worms' harmful behavior to this day. Our motivation is to make use of AtanganaBaleanu fractional derivative with Mittag-Leffler kernel which has latterly been brought into operation, and thus closely examine the basic SEIRA (susceptible-exposed-infectious-removed-antidotal) model associated with computer worms. To that end, we first prove the conditions that show the existence and uniqueness properties of the solutions for the fractional order model benefiting from fixed point theory. By using various values belonging to the fractional order, we also acquired different numerical simulations emphasizing that the aforementioned derivative is quite impactful.

References

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