On the Controllability of Coupled Nonlocal Partial Integrodifferential Equations Using Fractional Power Operators

In this research paper, we investigate the controllability in the $\alpha$-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.