Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series

Abstract

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.