Generalized fractional-order Bernoulli functions via Riemann-Liouville operator and their applications in the evaluation of Dirichlet series. (English) Zbl 1470.05019

Summary: In this work, we define a new class of functions of the Bernoulli type using the Riemann-Liouville fractional integral operator and derive a generating function for these class generalized functions. Then, these functions are employed to derive formulas for certain Dirichlet series.


05A15 Exact enumeration problems, generating functions
11B68 Bernoulli and Euler numbers and polynomials
26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
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