DOI: 10.1140/epjst/e2011-01388-0. Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics

10.1140/epjst/e2011-01388-0

Crossref journal-article

Springer Science and Business Media LLC

The European Physical Journal Special Topics (297)

Bibliography

de Oliveira, E. C., Mainardi, F., & Vaz, J. (2011). Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. The European Physical Journal Special Topics, 193(1), 161â171.

Authors 3

E. Capelas de Oliveira (first)
F. Mainardi (additional)
J. Vaz (additional)

References 31 Referenced 103

K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941) (10.1063/1.1750906) / J. Chem. Phys. by K.S. Cole (1941)
K.S. Cole, R.H. Cole, J. Chem. Phys. 10, 98 (1942) (10.1063/1.1723677) / J. Chem. Phys. by K.S. Cole (1942)
D.W. Davidson, R.H. Cole, J. Chem. Phys. 19, 1484 (1951) (10.1063/1.1748105) / J. Chem. Phys. by D.W. Davidson (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 (10.1017/CBO9780511662805)
H. Hilfer (ed.), Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000) (10.1142/3779)
A. Hanyga, M. Seredyńska, J. Stat. Phys. 131, 269 (2008) (10.1007/s10955-008-9501-7) / J. Stat. Phys. by A. Hanyga (2008)
S. Havriliak Jr., S. Negami, J. Polymer Sci. C 14, 99 (1966) (10.1002/polc.5070140111) / J. Polymer Sci. C by S. Havriliak Jr. (1966)
S. Havriliak, S. Negami, Polymer 8, 161 (1967) (10.1016/0032-3861(67)90021-3) / Polymer by S. Havriliak (1967)
A.K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectrics Press, London, 1983)
H. Hilfer, J. Non-Cryst. Solids 305, 122 (2002) (10.1016/S0022-3093(02)01088-8) / J. Non-Cryst. Solids by H. Hilfer (2002)
H. Hilfer, Phys. Rev. E 65, 061510/1 (2002) (10.1103/PhysRevE.65.061510) / Phys. Rev. E by H. Hilfer (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) (10.1142/p614)
A. Jurlewicz, K. Weron, J. Non-Cryst. Solids 305, 112 (2002) (10.1016/S0022-3093(02)01087-6) / J. Non-Cryst. Solids by A. Jurlewicz (2002)
A. Jurlewicz, K. Weron, M. Teuerle, Phys. Rev. E 78, 011103/1 (2008) (10.1103/PhysRevE.78.011103) / Phys. Rev. E by A. Jurlewicz (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] / Fract. Calculus Appl. Anal. by F. Mainardi (2007)
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) (10.2307/44153996) / Real Anal. Exchange by K.S. Miller (1997)
K.S. Miller, S.G. Samko, Integr. Trans. Spec. Funct. 12, 389 (2001) (10.1080/10652460108819360) / Integr. Trans. Spec. Funct. by K.S. Miller (2001)
V.V. Novikov, K.W. Wojciechowski, O.A. Komkova, T. Thiel, Mater. Sci. Poland 23, 977 (2005) / Mater. Sci. Poland by V.V. Novikov (2005)
I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)
H. Pollard, Bull. Amer. Math. Soc. 54, 1115 (1948) (10.1090/S0002-9904-1948-09132-7) / Bull. Amer. Math. Soc. by H. Pollard (1948)
T.R. Prabhakar, Yokohama Math. J. 19, 7 (1971) / Yokohama Math. J. by T.R. Prabhakar (1971)
W.R. Schneider, Expositiones Math. 14, 3 (1996) / Expositiones Math. by W.R. Schneider (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) (10.1016/j.jnoncrysol.2007.01.092) / J. Non-Cryst. Solids by B. Szabat (2007)
A. Stanislavsky, K. Weron, J. Trzmiel, Eur. Phys. Lett. (EPL) 91, 40003/1 (2010) / Eur. Phys. Lett. (EPL) by A. Stanislavsky (2010)
A.H. Zemanian, Realizability Theory for Continuous Linear Systems (Academic Press, San Diego, 1972)

Dates

Type	When
Created	14 years, 4 months ago (April 2, 2011, 7:31 a.m.)
Deposited	5 years, 2 months ago (June 17, 2020, 4:58 p.m.)
Indexed	2 days, 8 hours ago (Aug. 23, 2025, 9:32 p.m.)
Issued	14 years, 5 months ago (March 1, 2011)
Published	14 years, 5 months ago (March 1, 2011)
Published Online	14 years, 4 months ago (April 4, 2011)
Published Print	14 years, 5 months ago (March 1, 2011)

Funders 0

None

BibTeX

@article{de_Oliveira_2011, title={Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics}, volume={193}, ISSN={1951-6401}, url={http://dx.doi.org/10.1140/epjst/e2011-01388-0}, DOI={10.1140/epjst/e2011-01388-0}, number={1}, journal={The European Physical Journal Special Topics}, publisher={Springer Science and Business Media LLC}, author={de Oliveira, E. Capelas and Mainardi, F. and Vaz, J.}, year={2011}, month=mar, pages={161–171} }

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