A detailed analysis for the fundamental solution of fractional vibration equation

• Autorzy: Li-Li Liu , Jun-Sheng Duan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fractional derivatives and integrals; Fractional differential equations; Laplace transform; Fractionalvibration

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-09-13

zaakceptowano

2015-10-21

online

2015-11-26

Twórcy

autor

Li-Li Liu

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

autor

Jun-Sheng Duan

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

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Identyfikatory

DOI

10.1515/math-2015-0077