Modeling of pressure–volume controlled artificial respiration with local derivatives

Abstract We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative...

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Main Authors:	Bahar Acay, Mustafa Inc, Yu-Ming Chu, Bandar Almohsen
Format:	Article
Language:	English
Published:	SpringerOpen 2021-01-01
Series:	Advances in Difference Equations
Subjects:	Proportional derivative Local derivatives Clinical medicine Truncated M-derivative Conformable derivative
Online Access:	https://doi.org/10.1186/s13662-020-03204-9

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spelling	doaj-94c388f6e9594047b15104d14b3a07602021-01-17T12:52:21ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-012021112110.1186/s13662-020-03204-9Modeling of pressure–volume controlled artificial respiration with local derivativesBahar Acay0Mustafa Inc1Yu-Ming Chu2Bandar Almohsen3Department of Mathematics, Firat UniversityDepartment of Mathematics, Firat UniversityDepartment of Mathematics, Huzhou UniversityDepartment of Mathematics, King Saud UniversityAbstract We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.https://doi.org/10.1186/s13662-020-03204-9Proportional derivativeLocal derivativesClinical medicineTruncated M-derivativeConformable derivative
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bahar Acay Mustafa Inc Yu-Ming Chu Bandar Almohsen
spellingShingle	Bahar Acay Mustafa Inc Yu-Ming Chu Bandar Almohsen Modeling of pressure–volume controlled artificial respiration with local derivatives Advances in Difference Equations Proportional derivative Local derivatives Clinical medicine Truncated M-derivative Conformable derivative
author_facet	Bahar Acay Mustafa Inc Yu-Ming Chu Bandar Almohsen
author_sort	Bahar Acay
title	Modeling of pressure–volume controlled artificial respiration with local derivatives
title_short	Modeling of pressure–volume controlled artificial respiration with local derivatives
title_full	Modeling of pressure–volume controlled artificial respiration with local derivatives
title_fullStr	Modeling of pressure–volume controlled artificial respiration with local derivatives
title_full_unstemmed	Modeling of pressure–volume controlled artificial respiration with local derivatives
title_sort	modeling of pressure–volume controlled artificial respiration with local derivatives
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2021-01-01
description	Abstract We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.
topic	Proportional derivative Local derivatives Clinical medicine Truncated M-derivative Conformable derivative
url	https://doi.org/10.1186/s13662-020-03204-9
work_keys_str_mv	AT baharacay modelingofpressurevolumecontrolledartificialrespirationwithlocalderivatives AT mustafainc modelingofpressurevolumecontrolledartificialrespirationwithlocalderivatives AT yumingchu modelingofpressurevolumecontrolledartificialrespirationwithlocalderivatives AT bandaralmohsen modelingofpressurevolumecontrolledartificialrespirationwithlocalderivatives
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Modeling of pressure–volume controlled artificial respiration with local derivatives

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