Email this article As Integrais de Mellin-Barnes e a Função de Fox
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[1] R.F. Ávila, M.J. Menon, Eikonal zeros in the momentum transfer space from proton-proton scattering: An empirical analysis, Eur. Phys. J., 54C (2008), 555–576.
[2] B.L.J. Braaksma, Asymptotic expansions and analytical continuation for a class of Barnes-integrals, Compositio Math., 15 (1962), 239–341.
[3] E. Capelas de Oliveira, “Funções Especiais com Aplicações”, Editora Livraria da Física, São Paulo, 2005.
[4] E. Capelas de Oliveira, J. Vaz Jr., FS. Costa, The fractional Schrödinger equation for delta potentials, (2010), Journal of Mathematical Physics (aceito).
[5] E. Capelas de Oliveira, J. Vaz Jr., Tunneling in fractional quantum mechanics, (2010) Submetido à publicação.
[6] M. Caputo, Vibrations of an infinite viscoelastic layer with a dissipative memory, J. Acoust. Soc. Amer., 56 (1974), 897–904.
[7] W. Chen, S. Holm, Physical interpretation of fractional diffusion-wave equation via lossy media obeying frequency power law, arXiv.org/abs/math-ph/0303040 (2003).
[8] Debnath, Recent applications of fractional calculus to science and engineering, Int. J. Math., 2003 (2003), 3413–3442.
[9] A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, “Higher Transcendental Functions”, Vol.1, McGraw-Hill, New York, 1953.
[10] 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.
[11] R. Figueiredo Camargo, R. Charnet, E. Capelas de Oliveira, On some fractional Green’s functions, J. Math. Phys., 50 (2009), 043514.
[12] R. Figueiredo Camargo, E. Capelas de Oliveira, J. Vaz Jr., On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator, J. Math. Phys., 50 (2009), 123518.
[13] C. Fox, The G and H functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc., 98 (1961), 395–429.
[14] D. Gomes, E. Capelas de Oliveira, The generating function for Eℓ n (ρ) polynomials, Algebras, Groups and Geometries, 14 (1997) 49–57.
[15] P. Inizan, Homogeneous fractional embeddings, J. Math. Phys., 49 (2008), 082901.
[16] 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.
[17] V. Kiryakova, The special functions of fractional calculus as generalized fractional calculus operators of some basic functions, Comp. Math. Appl., 59 (2010), 1128–1141.
[18] G. Lauricella, Sulla funzione ipergeometrica a più variabili, Rend. Circ. Math. Palermo, 7 (1893), 111–158.
[19] E.K. Lenzi, L.R. Evangelista, M. K. Lenzi, H. V. Ribeiro and E. Capelas de Oliveira, Solutions of a Non-Markovian Diffusion Equation, Phys. Lett. A, 374 (2010) 4193–4198.
[20] C.F. Lorenzo, T.T. Hartley, Initialized fractional calculus, NASA/TP–2000–209943.
[21] F. Mainardi, “Fractional Calculus and Waves in Linear Viscoelasticity”, World Scientific Publishing Co., London, 2010.
[22] F. Mainardi, R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution process, J. Comput. Appl. Math., 118 (2000), 283–299.
[23] F. Mainardi, G. Pagnini, Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals, J. Comput. Appl. Math., 153 (2003), 331–342.
[24] F. Mainardi, G. Pagnini, R.K. Saxena, Fox H function in fractional diffusion, J. Comput. Appl. Math., 178 (2005), 321–331.
[25] A.M. Mathai, H.J. Haubold, “Special Functions for Applied Scientistic”, Springer, Heidelberg, 2008.
[26] A.M. Mathai, R.S. Saxena, H.J. Haubold, “The H−Function. Theory and Applications”, Springer, New York, 2010.
[27] G.S. Meijer, On the G function I-VIII, Nederl. Akad. Wettensch. Proc., 49, (1946), 227–237, 344–356, 457–469, 632–641, 765–772, 936–943, 1063–1072, 1165–1175. Traduzido para o Inglês: Indag. Math., 8, (1946), 124–134, 213– 225, 312–324, 391–400, 468–475, 595–602, 661–670 e 713–723.
[28] E.A. Notte Cuello, M.J. Menon, E. Capelas de Oliveira, Inverse problems in Hadron scattering and the Fox’s H−function (2010), Submetido à publicação.
[29] S. Pincherle, Sulle funzioni ipergeometriche generalizzate, Atti R. Accad. Lincei, Rend. Cl. Sci. Fis. Mat. Natur., 4 (1888), 694–700 e 792–799.
[30] I. Podlubny, “Fractional Differential Equations”, Mathematics in Science and Engineering, Vol.198, Academic Press, San Diego, 1999.
[31] T.R. Prabhakar, A singular integral equation with generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7–15.
[32] E.D. Rainville, “Special Function”, The Macmillan Company, New York, 1967.
[33] R.K. Saxena, In memorium of Charles Fox, Fract. Cal. Appl. Anal., 12 (2009), 337–344.
[34] I.N. Sneddon, “The Use of Integral Transforms”, McGraw-Hill, New York, 1972.
[35] Rui Yu, H. Zhang, New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation, Chaos, Solitons & Fractals, 30 (2006), 946–955.
[36] N.N. Temme, “Special Function: An Introduction to the Classical Functions of Mathematical Physics”, Wiley, New York, 1996.
DOI: https://doi.org/10.5540/tema.2011.012.02.0157
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