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This study develops a fractional phase framework for transient thermo viscoelastic vibrations of size-dependent uniaxial microbeams. Inherited damping, uncertain thermal loading, and micro scale stiffness effects are incorporated into a unified reduced-order model. The first mode reduction yields a fractional Kelvin Voight oscillator with temperature and size dependent effective stiffness. The fractional damping term is discretized using the L1 scheme, while the inertial dynamics is solved by central finite differences. Numerical results show that fractional order, thermal uncertainty, and size effects significantly affect the displacement and resonance behavior. The proposed model provides a transparent computational framework for coupling fractional dynamics, phase uncertainty, and vibration analysis at the micro/nano scale.
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