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The analysis of oscillatory properties of fractional circuits is still an open problem due to the multi-valuedness and non-locality of fractional operators. In this paper, the complex path integral approach is applied to achieve the impulsive response of fractional order RLCcircuit, which possesses the advantages of high precision and fast convergence as well as providing a novel way to the theoretical analysis of fractional order RLCcircuit. On this basis, the order dependent oscillation criterion (critical damping criterion) for fractional order RLCcircuit is successfully solved by adopting dimensionless analysis, and verified by the above proposed high accurate algorithm. Lastly, two examples are provided to validate and to show the advantages of the above conclusions. It should be highlighted that the approaches and conclusions of this paper are important supplements to the fractional order equivalent circuit modellings, and have important application values in engineering, viscoelastic materials and some other fields.

Dynamic response analysis of fractional order RLC α circuit and its order dependent oscillation criterion