Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel

Ramazan Ozarslan; Erdal Bas; Dumitru Baleanu; Bahar Acay; Ramazan Ozarslan; Erdal Bas; Dumitru Baleanu; Bahar Acay

doi:10.3934/math.2020031

AIMS Mathematics

2020, Volume 5, Issue 1: 467-481. doi: 10.3934/math.2020031

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Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel

1.
Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey
2.
Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey
3.
Institute of Space Sciences, Magurele-Bucharest, Romania

Received: 04 September 2019 Accepted: 28 November 2019 Published: 06 December 2019
MSC : 26A33, 97M50, 70E17

In this manuscript the fractional form of wind-influenced projectile motion equations which have a significant place in physics is extensively investigated by preserving dimensionality of the physical quantities for fractional operators and features of wind-influenced projectile motion are computed analytically in view of Atangana-Baleanu (ABC) fractional derivative in Caputo sense. Moreover, ABC fractional derivative with (n + α)th-order and its Laplace transform (LT) are obtained, α ∈ [0, 1] and n ∈ $\mathbb{N}$. A comparative analysis based on the classical case is carried out in order to shed more light on the potent of the ABC fractional operator. Hence we present the results for some values of α, k friction constant, different wind effects and different masses in 3D illustrations by comparing Caputo fractional operator. Thus, we can observe trajectory, time of flight, maximum height and range clearly. Moreover, the obtained results are shown to correspond to the classical case while the order α → 1.
- projectile motion,
- fractional model,
- Atangana-Baleanu fractional derivative,
- wind,
- drag
Citation: Ramazan Ozarslan, Erdal Bas, Dumitru Baleanu, Bahar Acay. Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel[J]. AIMS Mathematics, 2020, 5(1): 467-481. doi: 10.3934/math.2020031

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Abstract

In this manuscript the fractional form of wind-influenced projectile motion equations which have a significant place in physics is extensively investigated by preserving dimensionality of the physical quantities for fractional operators and features of wind-influenced projectile motion are computed analytically in view of Atangana-Baleanu (ABC) fractional derivative in Caputo sense. Moreover, ABC fractional derivative with (n + α)th-order and its Laplace transform (LT) are obtained, α ∈ [0, 1] and n ∈ $\mathbb{N}$. A comparative analysis based on the classical case is carried out in order to shed more light on the potent of the ABC fractional operator. Hence we present the results for some values of α, k friction constant, different wind effects and different masses in 3D illustrations by comparing Caputo fractional operator. Thus, we can observe trajectory, time of flight, maximum height and range clearly. Moreover, the obtained results are shown to correspond to the classical case while the order α → 1.

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