Impulsive psi-Caputo fractional equations involving operator pairs in Banach spaces

This article studies two classes of \(ψ\)-Caputo fractional equations with impulsive conditions and operator pairs in Banach spaces: one is the impulsive Sobolev-type integro-differential equations with operator pairs on bounded intervals, the other is the impulsive differential equations with operator pairs and finite delays on unbounded intervals. By combining the theory of propagating theory and the \(ψ\)-Laplace transform as well as fractional calculus, we firstly derive a proper definition of mild solutions for these impulsive equations. Depending on the definition, we establish existence and uniqueness theorems and a continuous dependence theorem for the impulsive integro-differential equations on bounded intervals. Next, we investigate the piecewise pseudo S-asymptotically \((ω,c)\)-periodic solutions for the impulsive delay equations on unbounded intervals. Finally, some examples are given to illustrate the main results. Here we do not assume the operator \(B\) has bounded or compact inverse \(B⁻¹\). Actually, our results are even new in the case when \(B=I\) and \(ψ(t)=t\). For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/86/abstr.html