This paper is devoted to study a class of semi-linear structural damped elastic systems with state dependent nonlocal condition on infinite intervals. Some new results about existence of mild solutions and classical solutions are established by introducing fractional power operator and using approximation theory and Schauder fixed point theorem. Finally, an example of structural damped beam vibration equation is given to verify the validity and feasibility of the abstract conclusions obtained. The results obtained in this paper essentially fill some gaps in this area.

In this paper, we discuss the existence of $IS$-asymptotically $\omega$-periodic mild L-quasi-solutions for a class of fractional evolution equations with non-instantaneous impulses. Under a new concept of upper and lower solutions, a new monotone iterative technique is constructed, and the necessary conditions for the existence of extremal coupled mild $L$-quasi-solutions are obtained. Finally, an example is given to illustrate the effectiveness of our theoretical results.