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Identification problems related to cylindrical dielectrics **in presence of polarization**
On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$
1. | Department of Physics and Astronomy, University of Bologna, and INFN, Via Irnerio 46, Bologna, I-40126, Italy |
References:
[1] |
Academic Press, New York, 1975. |
[2] |
World Scientific, Singapore, 2012.
doi: 10.1142/9789814355216. |
[3] |
Electron. J. Probab., 15 (2010), 684-709.
doi: 10.1214/EJP.v15-762. |
[4] |
Eur. Phys. J., Special Topics, 193 (2011) 161-171. [E-print arxiv.org/abs/1106.1761] Google Scholar |
[5] |
Pure and Appl. Geophys. (PAGEOPH), 91 (1971), 134-147. [Reprinted in Fract. Calc. Appl. Anal.,10 (2007), 309-324.] |
[6] |
Riv. Nuovo Cimento (Ser. II), 1 (1971), 161-198.
doi: 10.1007/BF02820620. |
[7] |
J. Chemical Physics, 10 (1942), 98-105.
doi: 10.1063/1.1723677. |
[8] |
The Principia Press, Bloomington, Indiana, 1936. Google Scholar |
[9] |
Springer, Lecture Notes in Mathematics No 2004, Heidelberg, 2010.
doi: 10.1007/978-3-642-14574-2. |
[10] |
Nauka, Moscow., 1966 [in Russian]. Google Scholar |
[11] |
Vol. III. Based, in part, on notes left by Harry Bateman. McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. |
[12] |
Vol. II, Second Edition, Wiley, New York, 1971. |
[13] |
{First Annual Report, NASA/TM-2002-211914}, Gleen Research Center, 2002, pp. XIV - 121. Google Scholar |
[14] |
Fract. Calc. Appl. Anal., 5 (2002), 491-518. |
[15] |
in Fractals and Fractional Calculus in Continuum Mechanics, (eds. A. Carpinteri and F. Mainardi), Springer Verlag, Wien, 1997, pp. 223-276. [E-print arxiv.org/abs/0805.3823] |
[16] |
J. Appl. Phys., 18 (1947), 212-221.
doi: 10.1063/1.1697606. |
[17] |
World Scientific, Singapore, 2000. Google Scholar |
[18] |
Ann. Math., 31 (1930), 479-528.
doi: 10.2307/1968241. |
[19] |
Fract. Calc. Appl. Anal., 16 (2013), 378-404.
doi: 10.2478/s13540-013-0024-9. |
[20] |
Differential and Integral Equations, 8 (1995), 993-1011. |
[21] |
Chapman and Hall/CRC, Boca Raton, FL, 2004.
doi: 10.1201/9780203487372. |
[22] |
Elsevier, Amsterdam, 2006. |
[23] |
Longman & J. Wiley, Harlow - New York, 1994. |
[24] |
Comp. Math. Appl., 59 (2010), 1885-1895.
doi: 10.1016/j.camwa.2009.08.025. |
[25] |
In American Institute of Physics - Conf. Proc., 1301 (2010), 597-613.
doi: 10.1063/1.3526661. |
[26] |
World Scientific, Singapore, 2012. |
[27] |
Begell House Publishers, Connecticut, 2006. Google Scholar |
[28] |
Imperial College Press, London and World Scientific, Singapore, 2010.
doi: 10.1142/9781848163300. |
[29] |
Fract. Calc. Appl. Anal., 10 (2007), 269-308. |
[30] |
Theory and Algorithmic Tables, Ellis Horwood, Chichester, 1983. |
[31] |
Springer, New York, 2008.
doi: 10.1007/978-0-387-75894-7. |
[32] |
Wiley Eastern Ltd, New Delhi, 1978. |
[33] |
Springer Verlag, New York, 2010.
doi: 10.1007/978-1-4419-0916-9. |
[34] |
Integral Transforms and Special Functions, 12 (2001), 389-402.
doi: 10.1080/10652460108819360. |
[35] |
Academic Press, San Diego, 1999. |
[36] |
Matlab-Code that calculates the Mittag-Leffler function with desired accuracy, Matlab File Exchange www.mathworks.com/matlabcentral/fileexchange, 2006. Google Scholar |
[37] |
Bull. Amer. Math. Soc., 54 (1948), 1115-1116.
doi: 10.1090/S0002-9904-1948-09132-7. |
[38] |
Gordon and Breach, Amsterdam, 1993. [English translation and revised version from the Russian edition, Integrals and Derivatives of Fractional Order and Some of Their Applications Nauka i Tekhnika, Minsk, 1987] |
[39] |
Fract. Calc. Appl. Anal., 15 (2012), 426-450.
doi: 10.2478/s13540-012-0031-2. |
[40] |
Vol. I. Holomorphic Functions, Nordhoff, Groningen, 1960. |
[41] |
2-nd ed., De Gruyter, Berlin, 2012.
doi: 10.1515/9783110269338. |
[42] |
Electron. J. Probab., 19 (2014), 1-25. [E-print arXiv:1310.1888]
doi: 10.1214/EJP.v19-3058. |
[43] |
South Asian Publishers, New Delhi and Madras, 1982. |
[44] |
Sbornik Mathematics, 198 (2007), 1011-1023.
doi: 10.1070/SM2007v198n07ABEH003871. |
[45] |
Springer, Berlin, 2010.
doi: 10.1007/978-3-642-14003-7. |
[46] |
Integral Transforms and Special Functions, 21 (2010), 797-814.
doi: 10.1080/10652461003675737. |
[47] |
Springer, Berlin, 2013.
doi: 10.1007/978-3-642-33911-0. |
[48] |
Constructive Approximation, 18 (2002), 355-385.
doi: 10.1007/s00365-001-0019-3. |
[49] |
E-print arXiv:1310.5592 [math.CA] (2013), pp. 17. Google Scholar |
show all references
References:
[1] |
Academic Press, New York, 1975. |
[2] |
World Scientific, Singapore, 2012.
doi: 10.1142/9789814355216. |
[3] |
Electron. J. Probab., 15 (2010), 684-709.
doi: 10.1214/EJP.v15-762. |
[4] |
Eur. Phys. J., Special Topics, 193 (2011) 161-171. [E-print arxiv.org/abs/1106.1761] Google Scholar |
[5] |
Pure and Appl. Geophys. (PAGEOPH), 91 (1971), 134-147. [Reprinted in Fract. Calc. Appl. Anal.,10 (2007), 309-324.] |
[6] |
Riv. Nuovo Cimento (Ser. II), 1 (1971), 161-198.
doi: 10.1007/BF02820620. |
[7] |
J. Chemical Physics, 10 (1942), 98-105.
doi: 10.1063/1.1723677. |
[8] |
The Principia Press, Bloomington, Indiana, 1936. Google Scholar |
[9] |
Springer, Lecture Notes in Mathematics No 2004, Heidelberg, 2010.
doi: 10.1007/978-3-642-14574-2. |
[10] |
Nauka, Moscow., 1966 [in Russian]. Google Scholar |
[11] |
Vol. III. Based, in part, on notes left by Harry Bateman. McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. |
[12] |
Vol. II, Second Edition, Wiley, New York, 1971. |
[13] |
{First Annual Report, NASA/TM-2002-211914}, Gleen Research Center, 2002, pp. XIV - 121. Google Scholar |
[14] |
Fract. Calc. Appl. Anal., 5 (2002), 491-518. |
[15] |
in Fractals and Fractional Calculus in Continuum Mechanics, (eds. A. Carpinteri and F. Mainardi), Springer Verlag, Wien, 1997, pp. 223-276. [E-print arxiv.org/abs/0805.3823] |
[16] |
J. Appl. Phys., 18 (1947), 212-221.
doi: 10.1063/1.1697606. |
[17] |
World Scientific, Singapore, 2000. Google Scholar |
[18] |
Ann. Math., 31 (1930), 479-528.
doi: 10.2307/1968241. |
[19] |
Fract. Calc. Appl. Anal., 16 (2013), 378-404.
doi: 10.2478/s13540-013-0024-9. |
[20] |
Differential and Integral Equations, 8 (1995), 993-1011. |
[21] |
Chapman and Hall/CRC, Boca Raton, FL, 2004.
doi: 10.1201/9780203487372. |
[22] |
Elsevier, Amsterdam, 2006. |
[23] |
Longman & J. Wiley, Harlow - New York, 1994. |
[24] |
Comp. Math. Appl., 59 (2010), 1885-1895.
doi: 10.1016/j.camwa.2009.08.025. |
[25] |
In American Institute of Physics - Conf. Proc., 1301 (2010), 597-613.
doi: 10.1063/1.3526661. |
[26] |
World Scientific, Singapore, 2012. |
[27] |
Begell House Publishers, Connecticut, 2006. Google Scholar |
[28] |
Imperial College Press, London and World Scientific, Singapore, 2010.
doi: 10.1142/9781848163300. |
[29] |
Fract. Calc. Appl. Anal., 10 (2007), 269-308. |
[30] |
Theory and Algorithmic Tables, Ellis Horwood, Chichester, 1983. |
[31] |
Springer, New York, 2008.
doi: 10.1007/978-0-387-75894-7. |
[32] |
Wiley Eastern Ltd, New Delhi, 1978. |
[33] |
Springer Verlag, New York, 2010.
doi: 10.1007/978-1-4419-0916-9. |
[34] |
Integral Transforms and Special Functions, 12 (2001), 389-402.
doi: 10.1080/10652460108819360. |
[35] |
Academic Press, San Diego, 1999. |
[36] |
Matlab-Code that calculates the Mittag-Leffler function with desired accuracy, Matlab File Exchange www.mathworks.com/matlabcentral/fileexchange, 2006. Google Scholar |
[37] |
Bull. Amer. Math. Soc., 54 (1948), 1115-1116.
doi: 10.1090/S0002-9904-1948-09132-7. |
[38] |
Gordon and Breach, Amsterdam, 1993. [English translation and revised version from the Russian edition, Integrals and Derivatives of Fractional Order and Some of Their Applications Nauka i Tekhnika, Minsk, 1987] |
[39] |
Fract. Calc. Appl. Anal., 15 (2012), 426-450.
doi: 10.2478/s13540-012-0031-2. |
[40] |
Vol. I. Holomorphic Functions, Nordhoff, Groningen, 1960. |
[41] |
2-nd ed., De Gruyter, Berlin, 2012.
doi: 10.1515/9783110269338. |
[42] |
Electron. J. Probab., 19 (2014), 1-25. [E-print arXiv:1310.1888]
doi: 10.1214/EJP.v19-3058. |
[43] |
South Asian Publishers, New Delhi and Madras, 1982. |
[44] |
Sbornik Mathematics, 198 (2007), 1011-1023.
doi: 10.1070/SM2007v198n07ABEH003871. |
[45] |
Springer, Berlin, 2010.
doi: 10.1007/978-3-642-14003-7. |
[46] |
Integral Transforms and Special Functions, 21 (2010), 797-814.
doi: 10.1080/10652461003675737. |
[47] |
Springer, Berlin, 2013.
doi: 10.1007/978-3-642-33911-0. |
[48] |
Constructive Approximation, 18 (2002), 355-385.
doi: 10.1007/s00365-001-0019-3. |
[49] |
E-print arXiv:1310.5592 [math.CA] (2013), pp. 17. Google Scholar |
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