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This paper investigates the dynamics of the beam-like structures whose response manifests a strong scale effect. The space-Fractional Euler-Bernoulli beam (s-FEB and space-Fractional Timoshenko beam (s-FT models, which are suitable for small-scale slender beams and small-scale thick beams, respectively, have been extended to a dynamic case. The study provides appropriate governing equations, numerical approximation, detailed analysis of free vibration, and experimental validation. The parametric study presents the influence of non-
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