Fractional physical models based on falling body problem

This article is devoted to investigate the fractional falling body problem relied on Newton's second law. We analyze this physical model by means of Atangana-Baleanu fractional derivative in the sense of Caputo (ABC), generalized fractional derivative introduced by Katugampola and generalized A...

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Main Authors:	Bahar Acay, Ramazan Ozarslan, Erdal Bas
Format:	Article
Language:	English
Published:	AIMS Press 2020-03-01
Series:	AIMS Mathematics
Subjects:	falling body problem physical model fractional calculus non-local operators fractional model
Online Access:	https://www.aimspress.com/article/10.3934/math.2020170/fulltext.html

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spelling	doaj-eafb61276d88424abd868aceaa28a96b2020-11-25T02:13:22ZengAIMS PressAIMS Mathematics2473-69882020-03-01532608262810.3934/math.2020170Fractional physical models based on falling body problemBahar Acay0Ramazan Ozarslan1Erdal Bas2Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, TurkeyDepartment of Mathematics, Science Faculty, Firat University, 23119 Elazig, TurkeyDepartment of Mathematics, Science Faculty, Firat University, 23119 Elazig, TurkeyThis article is devoted to investigate the fractional falling body problem relied on Newton's second law. We analyze this physical model by means of Atangana-Baleanu fractional derivative in the sense of Caputo (ABC), generalized fractional derivative introduced by Katugampola and generalized ABC containing the Mittag-Leffler function with three parameters $\mathbb{E}_{\alpha,\mu}^{\gamma}(.)$. For that purpose, the Laplace transform (LT) is utilized to obtain fractional solutions. In order to maintain the dimensionality of the physical parameter in the model, we employ an auxiliary parameter $\sigma$ having a relation with the order of fractional operator. Moreover, simulation analysis is carried out by comparing the underlying fractional derivatives with traditional one to grasp the virtue of the results.https://www.aimspress.com/article/10.3934/math.2020170/fulltext.htmlfalling body problemphysical modelfractional calculusnon-local operatorsfractional model
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bahar Acay Ramazan Ozarslan Erdal Bas
spellingShingle	Bahar Acay Ramazan Ozarslan Erdal Bas Fractional physical models based on falling body problem AIMS Mathematics falling body problem physical model fractional calculus non-local operators fractional model
author_facet	Bahar Acay Ramazan Ozarslan Erdal Bas
author_sort	Bahar Acay
title	Fractional physical models based on falling body problem
title_short	Fractional physical models based on falling body problem
title_full	Fractional physical models based on falling body problem
title_fullStr	Fractional physical models based on falling body problem
title_full_unstemmed	Fractional physical models based on falling body problem
title_sort	fractional physical models based on falling body problem
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2020-03-01
description	This article is devoted to investigate the fractional falling body problem relied on Newton's second law. We analyze this physical model by means of Atangana-Baleanu fractional derivative in the sense of Caputo (ABC), generalized fractional derivative introduced by Katugampola and generalized ABC containing the Mittag-Leffler function with three parameters $\mathbb{E}_{\alpha,\mu}^{\gamma}(.)$. For that purpose, the Laplace transform (LT) is utilized to obtain fractional solutions. In order to maintain the dimensionality of the physical parameter in the model, we employ an auxiliary parameter $\sigma$ having a relation with the order of fractional operator. Moreover, simulation analysis is carried out by comparing the underlying fractional derivatives with traditional one to grasp the virtue of the results.
topic	falling body problem physical model fractional calculus non-local operators fractional model
url	https://www.aimspress.com/article/10.3934/math.2020170/fulltext.html
work_keys_str_mv	AT baharacay fractionalphysicalmodelsbasedonfallingbodyproblem AT ramazanozarslan fractionalphysicalmodelsbasedonfallingbodyproblem AT erdalbas fractionalphysicalmodelsbasedonfallingbodyproblem
_version_	1724905661027844096

Fractional physical models based on falling body problem

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