A new nonlocal impulsive fractional differential hemivariational inclusions with an application to a frictional contact problem.

This paper is addressed to the study of a novel impulsive fractional differential hemivariational inclusions (IFDHI) with a nonlocal condition, comprising an impulsive fractional differential inclusion (IFDI) with a nonlocal condition and a hemivariational inequality (HVI), within separable reflexive Banach spaces. Initially, we establish the unique solvability of the HVI by adopting the surjectivity theorem for set-valued mappings. Subsequently, we demonstrate that there exist mild solutions for the new IFDHI by utilizing the theory of measure of noncompactness (MNC) and fixed point theorem (FPT) for condensing set-valued mappings. Additionally, we employ our principal findings to establish the solvability of a new frictional contact problem (FCP) concerning an elastic body interacting with a foundation within a finite time interval, considering the temperature effect. • A new nonlocal fractional impulsive evolution system is introduced and studied. • An existence of mild solutions is obtained for such a new system. • An application is given to a new frictional contact problem. [ABSTRACT FROM AUTHOR]