A theory of linear differential equations with fractional derivatives
T. M. Atanacković, S. Pilipović, B. Stanković (2012)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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T. M. Atanacković, S. Pilipović, B. Stanković (2012)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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Yakubovich, Semyon (2010)
International Journal of Mathematics and Mathematical Sciences
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Kiryakova, Virginia (2011)
Union of Bulgarian Mathematicians
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Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата. ...
B. Stanković (2011)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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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.
Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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Gupta, V.G., Shrama, Bhavna, Kiliçman, Adem (2010)
Journal of Applied Mathematics
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Huang, F. (2009)
Journal of Applied Mathematics
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Huang, X., Lu, X. (2010)
International Journal of Differential Equations
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Boyadjiev, Lyubomir, Kamenov, Ognian, Kalla, Shyam (2005)
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...
Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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