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2015 | 13 | 1 |

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A detailed analysis for the fundamental solution of fractional vibration equation

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In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case of 0 < α < 1, while y(t) is ultimately negative, and ultimately increases monotonically and approaches zero for the case of 1 < α < 2. We also consider the number of zeros, the maximum zero and the maximum extreme point of the fundamental solution y(t) for specified values of the coefficients and fractional order.








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  • School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, P.R. China
  • School of Sciences, Shanghai Institute of Technology, Shanghai 201418, P.R. China


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