Abstract

We prove the existence of at least one globally attractive mild solution to the equation partial derivative(t) (b * [x -h(., x(.))])(t) + A(x(t) - h (t,x(t))) = f(t, x(t)), t >= 0, under the assumption, among other hypothesis, that A is an almost sectorial operator on a Banach space X and the kernel b belongs to a large class, which covers many relevant cases from physics applications, in particular the important case of time- fractional evolution equations of neutral type.