Teorema de Adição para as Funçõoes de Mittag-Leffler
DOI:
https://doi.org/10.5540/tema.2009.010.01.0001Abstract
A partir do conceito de função de Green relativa à equação diferencial fracionária associada ao problema do telégrafo, apresentamos novas relações e um teorema de adição envolvendo as funções de Mittag-Leffler.References
[1] M. Caputo, Vibrations of an infinite viscoelastic layer with a dissipative memory, J. Acoust. Soc. Amer., 56 (1974), 897-904.
H. Chamati, N.S. Tonchev, Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction, J. Phys. A: Math. Gen., 39 (2006), 469-478.
Debnath, Recent applications of fractional calculus to Science and Engineering, Int. J. Math. 2003 (2003), 3413-3442.
R. Figueiredo Camargo, A.O. Chiacchio, E. Capelas de Oliveira, Differentiation to fractional orders and the fractional telegraph equation, J. Math. Phys., 49 (2008), 033505, [DOI 10.1063/1.2890375].
R. Figueiredo Camargo, “Do Teorema de Cauchy ao Método de Cagniard”, Dissertação de Mestrado, UNICAMP, Campinas, SP, 2005.
R. Figueiredo Camargo, E. Capelas de Oliveira, A.O. Chiacchio, “Sobre a Função de Mittag-Leffler”, R. P., 15/2006, UNICAMP, Campinas, SP, 2006.
T.T. Hartley, C.F. Lorenzo, A solution to the fundamental linear fractional order differential equation, NASA/TP - 1998-208693 (1998).
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, “Theory and Applications of Fractional Differential Equations”, Mathematics Studies, vol. 204, Edited by Jan van Mill, Elsevier, Amsterdam, 2006.
C.F. Lorenzo, T.T. Hartley, Initialized fractional calculus, NASA/TP - 2000-209943 (2000).
F. Mainardi, R. Gorenflo, On Mittag-Leffler-Type functions in fractional evolution process, J. Comput. Appl. Math., 118 (2000), 283-299.
I. Podlubny, “Fractional Differential Equations”, Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, 1999.
T.R. Prabhakar, A singular integral equation with generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7-15.
A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, “Integrals and Series”, vol. I, II, III, Elementary Functions, Gordon and Breach, New York, 1986.
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