Higher-order caputo fractional integrodifferential inclusions of Volterra–Fredholm type with impulses and infinite delay: existence results

This study explores a new type of impulsive nonlocal Caputo fractional dynamical differential inclusions of order 1<ϱ<2 in Banach space. The major goal is to identify mild solutions for impulsive nonlocal Caputo fractional Volterra–Fredholm integrodifferential inclusions with infinite delay. We use methods from fractional calculus, Dhage’s fixed-point concepts, integrodifferential equations, abstract phase space Bg, multivalued analysis, and sectorial operator of type (P,κ,ϱ,γ) to establish the necessary circumstances for the existence of mild solutions to these problems. Illustrative examples are provided to support the theoretical results and demonstrate their practical application.