Accepted for publication in JNEEA: Ms #2404252

On the existence of mild solutions for some nonlocal partial neutral integrodifferential equations in α-norm

Jaouad El Matloub and Khalil Ezzinbi

Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P: 2390 Marrakech, Morocco

Received on April 25, 2024
Accepted on May 3, 2024

Communicated by Gaston M. N'Guérékata

Abstract.  In this work, we study the existence of mild solutions in α-norm for a class of nonlocal neutral integrodifferential equations. Our approach relies on the utilization of a fixed-point theorem of Sadovskii-Krasnosel’skii type and the theory of resolvent operators.
Keywords: Mild solution, nonlocal condition, integrodifferential equation, α-norm, resolvent operator.
2010 Mathematics Subject Classification:   45K05; 47H10; 47D06.

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