Abstract.
We revisit the Mittag-Leffler functions of a real variable t, with one, two and three order-parameters {
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K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941)
K.S. Cole, R.H. Cole, J. Chem. Phys. 10, 98 (1942)
D.W. Davidson, R.H. Cole, J. Chem. Phys. 19, 1484 (1951)
K. Diethelm, An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer Lecture Notes in Mathematics No 2004 (Springer, Berlin, 2010)
G. Gripenberg, S.O. Londen, O.J. Staffans, Volterra Integral and Functional Equations (Cambridge University Press, Cambridge, 1990), p. 143
H. Hilfer (ed.), Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000)
A. Hanyga, M. Seredyńska, J. Stat. Phys. 131, 269 (2008)
S. Havriliak Jr., S. Negami, J. Polymer Sci. C 14, 99 (1966)
S. Havriliak, S. Negami, Polymer 8, 161 (1967)
A.K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectrics Press, London, 1983)
H. Hilfer, J. Non-Cryst. Solids 305, 122 (2002)
H. Hilfer, Phys. Rev. E 65, 061510/1 (2002)
A.K. Jonscher, Universal Relaxation Law (Chelsea Dielectrics Press, London, 1996)
F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity (Imperial College Press, London, 2010)
A. Jurlewicz, K. Weron, J. Non-Cryst. Solids 305, 112 (2002)
A. Jurlewicz, K. Weron, M. Teuerle, Phys. Rev. E 78, 011103/1 (2008)
A.M. Mathai, R.K. Saxena, H.J. Haubold, The H Function, Theory and Applications (Springer, Amsterdam, 2006)
I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)
F. Mainardi, R. Gorenflo, Fract. Calculus Appl. Anal. 10, 269 (2007) [E-print http://arxiv.org/abs/0801.4914]
A.H. Zemanian, Realizability Theory for Continuous Linear Systems (Academic Press, San Diego, 1972)
K.S. Miller, S.G. Samko, Real Anal. Exchange 23, 753 (1997)
K.S. Miller, S.G. Samko, Integr. Trans. Spec. Funct. 12, 389 (2001)
V.V. Novikov, K.W. Wojciechowski, O.A. Komkova, T. Thiel, Mater. Sci. Poland 23, 977 (2005)
I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)
H. Pollard, Bull. Amer. Math. Soc. 54, 1115 (1948)
T.R. Prabhakar, Yokohama Math. J. 19, 7 (1971)
W.R. Schneider, Expositiones Math. 14, 3 (1996)
R.T. Sibatov, D.V. Uchaikin [E-print: arXiv:1008.3972] 5 pages
B. Szabat, K. Weron, P. Hetman, J. Non-Cryst. Solids 353, 4601 (2007)
A. Stanislavsky, K. Weron, J. Trzmiel, Eur. Phys. Lett. (EPL) 91, 40003/1 (2010)
A.H. Zemanian, Realizability Theory for Continuous Linear Systems (Academic Press, San Diego, 1972)
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de Oliveira, E., Mainardi, F. & Vaz, J. Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. Eur. Phys. J. Spec. Top. 193, 161–171 (2011). https://doi.org/10.1140/epjst/e2011-01388-0
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DOI: https://doi.org/10.1140/epjst/e2011-01388-0