zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Entropies based on fractional calculus. (English) Zbl 1231.82024
Summary: We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except additivity. We show that this entropy function satisfies the Lesche and thermodynamic stability criteria.
MSC:
82B30Statistical thermodynamics
94A17Measures of information, entropy
60G22Fractional processes, including fractional Brownian motion
26A33Fractional derivatives and integrals (real functions)
References:
[1]Rényi, A.: Probability theory, (1970)
[2]Tsallis, C.: J. stat. Phys., J. stat. Phys. 52, 479 (1988)
[3]A list of works can be found in http://tsallis.cat.cbpf.br/biblio.htm
[4]Shafee, F.:
[5]Shafee, F.: IMA J. Appl. math., IMA J. Appl. math. 72, 785 (2007)
[6]Corless, R. M.; Gonnet, G. H.; Hare, D. E.; Jeffrey, D. J.; Knuth, D. E.: Adv. comput. Math., Adv. comput. Math. 5, 329 (1996)
[7]Kapur, J. N.; Kesavan, H. K.: Entropy optimization principles with applications, (1992)
[8], Entropy measures, maximum entropy principle and emerging applications (2003)
[9]Butzer, P. L.; Westphal, U.: An introduction to fractional calculus, Applications of fractional calculus in physics (2000) · Zbl 0987.26005
[10]Metzler, R.; Klafter, J.: Phys. rep., Phys. rep. 339, 1 (2000)
[11]Agrawal, O. P.: J. math. Anal. appl., J. math. Anal. appl. 272, 368 (2002)
[12]Herrmann, R.: Phys. lett. A, Phys. lett. A 372, 5515 (2008)
[13]Frederico, G. S. F.; Torres, D. F. M.: J. math. Anal. appl., J. math. Anal. appl. 334, 834 (2007)
[14]Abe, S.: Phys. lett. A, Phys. lett. A 224, 326 (1997)
[15]Jackson, F.: Quart. J. Pure appl. Math., Quart. J. Pure appl. Math. 41, 193 (1910)
[16]Ubriaco, M. R.: Phys. lett. A, Phys. lett. A 283, 157 (2001)
[17]Borges, E. P.; Rodity, I.: Phys. lett. A, Phys. lett. A 246, 399 (1998)
[18]Johal, R. S.: Phys. rev. E, Phys. rev. E 58, 4147 (1998)
[19]Lavagno, A.; Scarfone, A. M.; Swamy, P. Narayana: J. phys. A: math. Theor., J. phys. A: math. Theor. 40, 8635 (2007)
[20]Frank, T. D.; Daffertshofer, A.: Physica A, Physica A 285, 351 (2000)
[21]Lesche, B.: J. stat. Phys., J. stat. Phys. 27, 419 (1982)
[22]Lesche, B.: Phys. rev. E, Phys. rev. E 70, 017102 (2004)
[23]Abe, S.: Phys. rev. E, Phys. rev. E 66, 046134 (2002)
[24]Abe, S.; Kaniadakis, G.; Scarfone, A. M.: J. phys. A: math. Gen., J. phys. A: math. Gen. 37, 10513 (2004)
[25]Scarfone, A. M.; Wada, T.: Phys. rev. E, Phys. rev. E 72, 026123 (2005)
[26]Oikonomou, Th.: Physica A, Physica A 381, 155 (2007)
[27]Wada, T.: Physica A, Physica A 340, 126 (2004)
[28]Ubriaco, M. R.: Phys. rev. E, Phys. rev. E 62, 328 (2000)
[29]Büyükkiliç, F.; Demirhan, D.; Düleç, A.: Phys. lett. A, Phys. lett. A 197, 209 (1995)
[30]Pal, N. R.; Pal, S. K.: IEE trans. Syst. man. Cybern., IEE trans. Syst. man. Cybern. 21, 1260 (1991)