Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces

Abstract

In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem, we present sufficient criteria ensuring the controllability of the given problem. An illustrative example is also discussed.

Keywords

• integrodifferential equation
• mild solution
• measures of noncompactness
• resolvent operator controllability
• fixed point theorem
• fréchet space