Abstract
Entropy gives the irregularity of physical systems and also gives the
amount of information that cannot be understood in digital systems. For this
purpose, the definition of entropy was made by Shannon for digital data. The
definition of entropy using the concept of fractional order derivative was made
by Karcı. In this study, the results of Karcı and Shannon entropy definitions
in different probability environments were compared.
Keywords
References
- [1] C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379–423, 623–656.[2] S. Bouzebda, I. Elhattab, New Kernel-types Estimator of Shannon’s Entropy, Comptes Rendus Mathematique, vol. 352, Comptes Rendus de l’Académiedes Sciences–Series I–Mathematics, 2014, pp. 75–80.[3] M.R. Ubriaco, Entropies based on fractional calculus, Phys. Lett. A 373 (2009) 2516–2519.[4] A. Karcı, A new approach for fractional order derivative and its applications, Univ. J. Eng. Sci. 1 (2013) 110–117.[5] A. Karcı, Properties of fractional order derivatives for groups of relations/functions, Univ. J. Eng. Sci. 3 (2015) 39–45.[6] A. Karcı, The linear, nonlinear and partial differential equations are not fractional order differential equations, Univ. J. Eng. Sci. 3 (2015) 46–51.[7] A. Karcı, Generalized fractional order derivatives for products and quotients, Sci. Innov. 3 (2015) 58–62.[8] A. Karcı, Chain rule for fractional order derivatives, Sci. Innov. 3 (2015) 63–67.[9] A. Karcı, “Fractional order entropy New perspectives”, Optik - International Journal for Light and Electron Optics, vol:127, no:20, pp:9172-9177, 2016.
Abstract
Entropi, fiziksel sistemlerin düzensizliğini, dijital sistemler de ise,
anlam verilememiş bilgi miktarını vermektedir. Bu amaçla Shannon tarafından
dijital veriler için entropi tanımı yapılmıştır. Kesir dereceli türev kavramı
kullanılarak entropi tanımı ise Karcı tarafından yapılmıştır. Bu çalışmada
Karcı ve Shannon entropi tanımlarının farklı olasılık ortamlarında vermiş
oldukları sonuçların karşılaştırmaları yapılmıştır.
Keywords
References
- [1] C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379–423, 623–656.[2] S. Bouzebda, I. Elhattab, New Kernel-types Estimator of Shannon’s Entropy, Comptes Rendus Mathematique, vol. 352, Comptes Rendus de l’Académiedes Sciences–Series I–Mathematics, 2014, pp. 75–80.[3] M.R. Ubriaco, Entropies based on fractional calculus, Phys. Lett. A 373 (2009) 2516–2519.[4] A. Karcı, A new approach for fractional order derivative and its applications, Univ. J. Eng. Sci. 1 (2013) 110–117.[5] A. Karcı, Properties of fractional order derivatives for groups of relations/functions, Univ. J. Eng. Sci. 3 (2015) 39–45.[6] A. Karcı, The linear, nonlinear and partial differential equations are not fractional order differential equations, Univ. J. Eng. Sci. 3 (2015) 46–51.[7] A. Karcı, Generalized fractional order derivatives for products and quotients, Sci. Innov. 3 (2015) 58–62.[8] A. Karcı, Chain rule for fractional order derivatives, Sci. Innov. 3 (2015) 63–67.[9] A. Karcı, “Fractional order entropy New perspectives”, Optik - International Journal for Light and Electron Optics, vol:127, no:20, pp:9172-9177, 2016.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | PAPERS |
| Authors | |
| Publication Date | December 1, 2019 |
| Submission Date | December 23, 2018 |
| Acceptance Date | May 3, 2019 |
| Published in Issue | Year 2019 Volume: 4 Issue: 2 |
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