This compilation introduces and studies the class of (asymptotically) Stepanov almost automorphic functions with variable exponents, presenting a few relevant applications of abstract Volterra integro-differential inclusions in Banach spaces. The authors study the existence and regularity of solutions for some nonlinear second order differential equations, showing the existence of mild solutions and giving sufficient conditions ensuring the existence of strict solutions. Sufficient conditions for the oscillation of solutions of neutral impulsive differential equations are also presented. In the penultimate study, the oscillatory behaviour of the solutions of a class of nonlinear first-order neutral differential equations with several delays of one form are studied. In addition, some sufficient conditions for the oscillation of solutions to the first and second-order neutral delay difference equation are presented.