This paper studies a class of first-order abstract integro-differential inclusions defined on a Banach space. Our system is characterized by time-varying evolution operators and, notably, nonlocal initial conditions formulated as set inclusions. The motivation for this research stems from the need for more accurate modeling of complex physical and biological systems exhibiting memory effects, where traditional local or single-valued nonlocal conditions prove insufficient. Employing techniques from resolvent operator theory, fixed point arguments involving measures of non-compact-ness, and the ...
