*Article* **Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses**

#### **Mouffak Benchohra 1,2, Noreddine Rezoug 1, Bessem Samet 2 and Yong Zhou 3,4,\***


Received: 18 August 2019; Accepted: 12 November 2019; Published: 20 November 2019

**Abstract:** We consider a non-instantaneous system represented by a second order nonlinear differential equation in a Banach space *E*. We use the family of linear bounded operators introduced by Kozak, Darbo fixed point method and Kuratowski measure of noncompactness. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results.

**Keywords:** second order differential equations; mild solution; non-instantaneous impulses; Kuratowski measure of noncompactness; Darbo fixed point
