Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions
In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order $\beta\in(1,2]$ subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous $\beta$-order fractiona...
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doaj-81a4575859cd4c9282d46b6fa426b3fd2021-01-07T02:50:15ZengUniversidad de La FronteraCubo0716-77760719-06462020-12-0122336137710.4067/S0719-06462020000300361Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditionsAbdeldjalil Aouane0https://orcid.org/0000-0002-3654-6238Smaïl Djebali1https://orcid.org/0000-0002-2318-1989Mohamed Aziz Taoudi2https://orcid.org/0000-0002-8851-8714Département de Sciences Exactes et Informatique, École Normale Supérieure, Constantine, Algeria. – Laboratoire Théorie du Point Fixe et Applications ENS, BP 92 Kouba, Algiers, 16006. Algeria.Department of Mathematics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), PB 90950. Riyadh 11623, Saudi Arabia. – Laboratoire Théorie du Point Fixe et Applications ENS, BP 92 Kouba, Algiers, 16006. Algeria.Cadi Ayyad University, National School of Applied Science Marrakesh, Morocco.In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order $\beta\in(1,2]$ subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous $\beta$-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.http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2470/2027cosine operatorfractional integro-differential operatorabstract differential equationnoncompact nonlocal condition |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Abdeldjalil Aouane Smaïl Djebali Mohamed Aziz Taoudi |
spellingShingle |
Abdeldjalil Aouane Smaïl Djebali Mohamed Aziz Taoudi Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions Cubo cosine operator fractional integro-differential operator abstract differential equation noncompact nonlocal condition |
author_facet |
Abdeldjalil Aouane Smaïl Djebali Mohamed Aziz Taoudi |
author_sort |
Abdeldjalil Aouane |
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 |
series |
Cubo |
issn |
0716-7776 0719-0646 |
publishDate |
2020-12-01 |
description |
In this paper, we prove the existence of mild solutions of a class of fractional semilinear integro-differential equations of order $\beta\in(1,2]$ subjected to noncompact initial nonlocal conditions. We assume that the linear part generates an arbitrarily strongly continuous $\beta$-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. |
topic |
cosine operator fractional integro-differential operator abstract differential equation noncompact nonlocal condition |
url |
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2470/2027 |
work_keys_str_mv |
AT abdeldjalilaouane mildsolutionsofaclassofsemilinearfractionalintegrodifferentialequationssubjectedtononcompactnonlocalinitialconditions AT smaildjebali mildsolutionsofaclassofsemilinearfractionalintegrodifferentialequationssubjectedtononcompactnonlocalinitialconditions AT mohamedaziztaoudi mildsolutionsofaclassofsemilinearfractionalintegrodifferentialequationssubjectedtononcompactnonlocalinitialconditions |
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1724346852948574208 |