Elements for a new information theory based on fractional calculus via modified Riemann-Liouville derivative (Q2923077)
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scientific article; zbMATH DE number 6355824
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elements for a new information theory based on fractional calculus via modified Riemann-Liouville derivative |
scientific article; zbMATH DE number 6355824 |
Statements
15 October 2014
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informational entropy
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Shannon entropy
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fractional calculus
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Mittag-Leffler function
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generalized entropy
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Fisher information
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coarse graining
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amplitude of probability
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entropy of non-random functions
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Elements for a new information theory based on fractional calculus via modified Riemann-Liouville derivative (English)
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This paper consists of a collection of some basic definitions and ideas on information theory using the approach of fractional calculus and Riemann-Liouville derivatives. In particular, by studying the functional equation \(f^{\beta}(xy)\geq f^{\beta}(x) +f^{\beta}(y), \beta >1,\) the author derived a family of solutions which are exactly the inverse of the Mittag-Leffler function. The results obtained are used to describe a new family of generalized informational entropies via fractional calculus.
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