Anomalous diffusion resulted from fractional damping

Highlights: • The random process of a Brownian particle diffusion in a pure fractional damping environment is studied for the first time. • Several anomalous behaviors are revealed such as that a type of reverse diffusion is encountered. • The diffusion dynamics is closely related to the fractional exponent α. • Particles are found to move reversely in the opposite direction of diffusion when α is relatively large despite of the zero-approximating effective friction of the system. - Abstract: The dynamics of a Brownian particle diffusing in the pure fractional damping environment is studied in the field of a metastable potential. Several anomalous behaviors are revealed such as that a type of reverse diffusion is encountered. And the diffusion dynamics is closely related to the fractional exponent α. Particles are found to move reversely in the opposite direction of diffusion when α is relatively large despite of the zero-approximating effective friction of the system