Oscillation of functional differential equations with a delayed damping term: Enhanced criteria and numerical simulation

This study aims to derive criteria for examining the asymptotic and oscillatory behavior of solutions to functional differential equations with delayed damping. By employing the Riccati technique together with an improved approach, we establish new criteria that complement the existing literature while distinguishing themselves by accounting for the delay effect in the damping term and by providing the well-known sharp criterion for Euler-type equations. Numerical examples illustrate the theoretical findings and clarify how the delay in the damping term affects the solution dynamics.