A note on fractional Sumudu transform.
Gupta, V.G., Shrama, Bhavna, Kiliçman, Adem (2010)
Journal of Applied Mathematics
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Gupta, V.G., Shrama, Bhavna, Kiliçman, Adem (2010)
Journal of Applied Mathematics
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Yakubovich, Semyon (2010)
International Journal of Mathematics and Mathematical Sciences
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B. Stanković (2011)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Li, Changpin, Qian, Deliang, Chen, Yangquan (2011)
Discrete Dynamics in Nature and Society
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Huang, F. (2009)
Journal of Applied Mathematics
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Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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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...
Anastassiou, G.A., Koliha, J.J., Peǎrić, J. (2002)
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.
Shu Qin Zhang (2008)
Mathematica Bohemica
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Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.
B. Stanković (2010)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Nikolova, Yanka (2012)
Mathematica Balkanica New Series
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MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45 We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem...