Fractional calculus, zeta functions and Shannon entropy - Guariglia, Emanuel [UNESP] (De Gruyter, 2021)
This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ \zeta 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.
Keywords: Bernoulli numbers; fractional derivative; functional equation; Hurwitz ζ function; Shannon entropy