Asymptotically $(w,c)$-almost periodic type solutions of abstract degenerate non-scalar Volterra equations

We analyze asymptotically $(w, c)$-almost periodic type solutions of abstract degenerate non-scalar Volterra equations in Banach spaces. In order to do that, we primarily consider the exponentially decaying rate of $(A, k, B)$-regularized $C$-pseudoresolvent families. We illustrate the obtained results with some examples and possible applications.