On Riemann-Liouville and Caputo derivatives.
Li, Changpin, Qian, Deliang, Chen, Yangquan (2011)
Discrete Dynamics in Nature and Society
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Li, Changpin, Qian, Deliang, Chen, Yangquan (2011)
Discrete Dynamics in Nature and Society
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Li-Li Liu, Jun-Sheng Duan (2015)
Open Mathematics
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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...
Yakar, Coşkun, Yakar, Ali (2010)
Abstract and Applied Analysis
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Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Helena Musielak (1973)
Colloquium Mathematicae
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Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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Samuel, M., Thomas, Anitha (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
B. Martić (1964)
Matematički Vesnik
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Branislav Martić (1973)
Publications de l'Institut Mathématique
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Masayoshi Hata (2005)
Acta Arithmetica
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Huang, F. (2009)
Journal of Applied Mathematics
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