$Differential equations with tempered Ψ-Caputo fractional derivative$
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Differential equations with tempered Ψ-Caputo fractional derivative

In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this ty...

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Main Authors:	Milan Medveď, Eva Brestovanská
Format:	article
Language:	EN
Published:	Vilnius Gediminas Technical University 2021
Subjects:	tempered riemann-liouville fractional derivative tempered ψ−caputo fractional derivative Mathematics QA1-939
Online Access:	https://doaj.org/article/42e9b25dc4094632b9320576e97d6b37
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id	oai:doaj.org-article:42e9b25dc4094632b9320576e97d6b37
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spelling	oai:doaj.org-article:42e9b25dc4094632b9320576e97d6b372021-11-29T09:14:00ZDifferential equations with tempered Ψ-Caputo fractional derivative1392-62921648-351010.3846/mma.2021.13252https://doaj.org/article/42e9b25dc4094632b9320576e97d6b372021-11-01T00:00:00Zhttps://journals.vgtu.lt/index.php/MMA/article/view/13252https://doaj.org/toc/1392-6292https://doaj.org/toc/1648-3510In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.Milan MedveďEva BrestovanskáVilnius Gediminas Technical Universityarticletempered riemann-liouville fractional derivativetempered ψ−caputo fractional derivativeMathematicsQA1-939ENMathematical Modelling and Analysis, Vol 26, Iss 4, Pp 631-650 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	tempered riemann-liouville fractional derivative tempered ψ−caputo fractional derivative Mathematics QA1-939
spellingShingle	tempered riemann-liouville fractional derivative tempered ψ−caputo fractional derivative Mathematics QA1-939 Milan Medveď Eva Brestovanská Differential equations with tempered Ψ-Caputo fractional derivative
description	In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.
format	article
author	Milan Medveď Eva Brestovanská
author_facet	Milan Medveď Eva Brestovanská
author_sort	Milan Medveď
title	Differential equations with tempered Ψ-Caputo fractional derivative
title_short	Differential equations with tempered Ψ-Caputo fractional derivative
title_full	Differential equations with tempered Ψ-Caputo fractional derivative
title_fullStr	Differential equations with tempered Ψ-Caputo fractional derivative
title_full_unstemmed	Differential equations with tempered Ψ-Caputo fractional derivative
title_sort	differential equations with tempered ψ-caputo fractional derivative
publisher	Vilnius Gediminas Technical University
publishDate	2021
url	https://doaj.org/article/42e9b25dc4094632b9320576e97d6b37
work_keys_str_mv	AT milanmedved differentialequationswithtemperedpscaputofractionalderivative AT evabrestovanska differentialequationswithtemperedpscaputofractionalderivative
_version_	1718407396772020224

Differential equations with tempered Ψ-Caputo fractional derivative

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