$Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay$
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Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay

In this paper, we prove the existence and uniqueness of a mild solution to the system of ψ- Hilfer neutral fractional evolution equations with infinite delay H𝔻0αβ;ψ [x(t) − h(t, xt)] = A x(t) + f (t, x(t), xt), t ∈ [0, b], b > 0 and x(t) = ϕ(t), t ∈ (−∞, 0]. We first obtain the Volterra integral...

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Auteurs principaux:	Norouzi Fatemeh, N’guérékata Gaston M.
Format:	article
Langue:	EN
Publié:	De Gruyter 2021
Sujets:	ψ-hilfer fractional derivative infinite delays mild solution banach contraction principle leray-schauder alternative 34a08 34a12 34g99 34k99 Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/e4a4486e9e1245a19b33d1381d28a8d0
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id	oai:doaj.org-article:e4a4486e9e1245a19b33d1381d28a8d0
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spelling	oai:doaj.org-article:e4a4486e9e1245a19b33d1381d28a8d02021-12-05T14:10:56ZExistence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay2353-062610.1515/msds-2020-0128https://doaj.org/article/e4a4486e9e1245a19b33d1381d28a8d02021-04-01T00:00:00Zhttps://doi.org/10.1515/msds-2020-0128https://doaj.org/toc/2353-0626In this paper, we prove the existence and uniqueness of a mild solution to the system of ψ- Hilfer neutral fractional evolution equations with infinite delay H𝔻0αβ;ψ [x(t) − h(t, xt)] = A x(t) + f (t, x(t), xt), t ∈ [0, b], b > 0 and x(t) = ϕ(t), t ∈ (−∞, 0]. We first obtain the Volterra integral equivalent equation and propose the mild solution of the system. Then, we prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem.Norouzi FatemehN’guérékata Gaston M.De Gruyterarticleψ-hilfer fractional derivativeinfinite delaysmild solutionbanach contraction principleleray-schauder alternative34a0834a1234g9934k99MathematicsQA1-939ENNonautonomous Dynamical Systems, Vol 8, Iss 1, Pp 101-124 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	ψ-hilfer fractional derivative infinite delays mild solution banach contraction principle leray-schauder alternative 34a08 34a12 34g99 34k99 Mathematics QA1-939
spellingShingle	ψ-hilfer fractional derivative infinite delays mild solution banach contraction principle leray-schauder alternative 34a08 34a12 34g99 34k99 Mathematics QA1-939 Norouzi Fatemeh N’guérékata Gaston M. Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay
description	In this paper, we prove the existence and uniqueness of a mild solution to the system of ψ- Hilfer neutral fractional evolution equations with infinite delay H𝔻0αβ;ψ [x(t) − h(t, xt)] = A x(t) + f (t, x(t), xt), t ∈ [0, b], b > 0 and x(t) = ϕ(t), t ∈ (−∞, 0]. We first obtain the Volterra integral equivalent equation and propose the mild solution of the system. Then, we prove the existence and uniqueness of solution by using the Banach contraction mapping principle and the Leray-Schauder alternative theorem.
format	article
author	Norouzi Fatemeh N’guérékata Gaston M.
author_facet	Norouzi Fatemeh N’guérékata Gaston M.
author_sort	Norouzi Fatemeh
title	Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay
title_short	Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay
title_full	Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay
title_fullStr	Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay
title_full_unstemmed	Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay
title_sort	existence results to a ψ- hilfer neutral fractional evolution equation with infinite delay
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/e4a4486e9e1245a19b33d1381d28a8d0
work_keys_str_mv	AT norouzifatemeh existenceresultstoapshilferneutralfractionalevolutionequationwithinfinitedelay AT nguerekatagastonm existenceresultstoapshilferneutralfractionalevolutionequationwithinfinitedelay
_version_	1718371573569683456

Existence results to a ψ- Hilfer neutral fractional evolution equation with infinite delay

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