January 1, 2021Open Access

Fractional calculus, zeta functions and Shannon entropy

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Abstract

Abstract This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative. We state and prove the functional equation together with an integral representation by Bernoulli numbers. Moreover, we treat an application in terms of Shannon entropy.

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Emanuel Guariglia (Fri,) studied this question.

synapsesocial.com/papers/69dff7ed1827a1d0b1255aa0 https://doi.org/https://doi.org/10.1515/math-2021-0010

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