Abstract
In this research paper, we investigate the controllability in the α-norm of a coupled system of integrodifferential equations with state-dependent nonlocal conditions in generalized Banach spaces. We establish sufficient conditions for the system’s controllability using resolvent operator theory introduced by Grimmer, fractional power operators, and fixed-point theorems associated with generalized measures of noncompactness for condensing operators in vector Banach spaces. Finally, we present an application example to validate the proposed methodology in this research.
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