Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions

In this paper, we investigated Caputo fractional integro-differential equations with non-instantaneous impulses and nonlocal conditions. By employing the solution operator, the Mönch fixed point theorem, and the stepwise estimation method, we eliminated the Lipschitz condition of the nonlinear term, while also dispensing with the requirement for the compressibility coefficient condition $0<k<1$. The main results presented represented a generalization and enhancement of previous findings. Furthermore, an example was provided to verify the application of our main results.