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

Author
Aouane, Abdeldjalil

Djebali, Smaïl

Taoudi, Mohamed Aziz

Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2470
10.4067/S0719-06462020000300361
Abstract
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 Carathéodory 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.
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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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