Existence and Controllability Results for Integrodifferential Equations with State-Dependent Nonlocal Conditions via Fractional Power Operators in Fréchet Spaces

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发表日期：

2024年5月4日

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Hamida Litimein,
Zhen-You Huang,
Abdelkrim Salim,
Mouffak Benchohra

摘要

In this work, we investigate the existence of mild solutions and controllability of integrodifferential equations subject to a state-dependent nonlocal condition on an unbounded interval in the $\alpha $ $α$ -norm, all under the assumption of noncompactness of the resolvent operator. To address this problem, we apply fractional power operators and a generalization of Darbo’s fixed-point theorem for Fréchet spaces, incorporating the concept of measures of noncompactness.