$Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions$
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Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions

Abstract In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order β ∈ (1, 2] subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous...

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Autores principales:	Aouane,Abdeldjalil, Djebali,Smaïl, Taoudi,Mohamed Aziz
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2020
Materias:	Cosine operator fractional integro-differential operator, abstract differential equation noncompact nonlocal condition
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300361
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spelling	oai:scielo:S0719-064620200003003612020-12-30Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditionsAouane,AbdeldjalilDjebali,SmaïlTaoudi,Mohamed Aziz Cosine operator fractional integro-differential operator, abstract differential equation noncompact nonlocal condition Abstract In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order β ∈ (1, 2] subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous β-order fractional cosine family, while the nonlinear forcing term is of Carath´eodory type and satisfies some fairly general growth conditions. Our approach combines the Monch fixed point theorem with some recent results regarding the measure of noncompactness of integral operators. Our conclusions improve and generalize many earlier related works. An example is provided to illustrate the main results.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.22 n.3 20202020-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300361en10.4067/S0719-06462020000300361
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Cosine operator fractional integro-differential operator, abstract differential equation noncompact nonlocal condition
spellingShingle	Cosine operator fractional integro-differential operator, abstract differential equation noncompact nonlocal condition Aouane,Abdeldjalil Djebali,Smaïl Taoudi,Mohamed Aziz Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
description	Abstract In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order β ∈ (1, 2] subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous β-order fractional cosine family, while the nonlinear forcing term is of Carath´eodory type and satisfies some fairly general growth conditions. Our approach combines the Monch fixed point theorem with some recent results regarding the measure of noncompactness of integral operators. Our conclusions improve and generalize many earlier related works. An example is provided to illustrate the main results.
author	Aouane,Abdeldjalil Djebali,Smaïl Taoudi,Mohamed Aziz
author_facet	Aouane,Abdeldjalil Djebali,Smaïl Taoudi,Mohamed Aziz
author_sort	Aouane,Abdeldjalil
title	Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
title_short	Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
title_full	Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
title_fullStr	Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
title_full_unstemmed	Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
title_sort	mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300361
work_keys_str_mv	AT aouaneabdeldjalil mildsolutionsofaclassofsemilinearfractionalintegrodifferentialequationssubjectedtononcompactnonlocalinitialconditions AT djebalismail mildsolutionsofaclassofsemilinearfractionalintegrodifferentialequationssubjectedtononcompactnonlocalinitialconditions AT taoudimohamedaziz mildsolutionsofaclassofsemilinearfractionalintegrodifferentialequationssubjectedtononcompactnonlocalinitialconditions
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Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions

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