Malatya Functions: Symmetric Functions Obtained by Applying Fractional Order Derivative to Karcı Entropy

Yıl 2017, Cilt: 2 Sayı: 2, 1 - 8, 30.12.2017

Ali Karci

Öz

Shannon
applied derivative to a special probability function and obtained entropy
definition. Karcı converted the derivative with fractional order derivative and
obtained a new definition for entropy. In this study, the fractional order of
derivative were selected as complex number and symmetric function were
obtained. Some of them were illustrated in this study, and it is known that
there are infinite symmetric functions obtained by this way.

Anahtar Kelimeler

Fractional Calculus, Fractional Order Derivative, Entropy, Symmetric Functions

Kaynakça

• [1] S. Das, Functional Fractional Calculus, Springer-Verlag Berlin Heidelberg, (2011).
• [2] A. Karcı, “A New Approach for Fractional Order Derivative and Its Applications”, Universal Journal of Engineering Sciences, Vol:1, pp: 110-117, 2013.
• [3] A. Karcı, “Properties of Fractional Order Derivatives for Groups of Relations/Functions”, Universal Journal of Engineering Sciences, vol:3, pp:39-45, 2015.
• [4] A. Karcı,”The Linear, Nonlinear and Partial Differential Equations are not Fractional Order Differential Equations”, Universal Journal of Engineering Sciences, vol:3, pp:46-51, 2015.
• [5] A. Karcı, “Generalized Fractional Order Derivatives for Products and Quotients”, Science Innovation, vol:3, pp:58-62, 2015.
• [6] A. Karcı, “Chain Rule for Fractional Order Derivatives”, Science Innovation, vol:3, 63-67, 2015.
• [7] S. Bouzebda, I. Elhattab, “New Kernel-types Estimator of Shannon’s Entropy”, Comptes Rendus Mathematique (Comptes Rendus de l'Académie des Sciences - Series I - Mathematics), vol:352, pp:75-80, 2014.
• [8] M. R.Ubriaco, “Entropies based on fractional calculus”, Physics Letters A, vol:373, pp: 2516-2519, 2009.
• [9] A. Karcı, “Fractional order entropy New perspectives”, Optik - International Journal for Light and Electron Optics, vol:127, no:20, pp:9172-9177, 2016. [10] A. Karcı, “New Kinds of Entropy Fractional Entropy”, International Conference on Natural Science and Engineering, 1-4, 2016.