Fractional Calculus of the Lerch Zeta Function - Guariglia, Emanuel [UNESP] (Springer Nature, 2022)
This paper deals with the fractional derivative of the Lerch zeta function. We compute the fractional derivative of the Lerch zeta function using a complex generalization of the Grünwald–Letnikov derivative. This definition of fractional derivative, fulfilling the generalized Leibniz rule, allows us to derive a functional equation for the fractional derivative of the Lerch zeta function. This functional equation is rewritten in a simplified form that reduces its computational cost. Furthermore, we prove an approximate functional equation for the fractional derivative of the Lerch zeta function.
Keywords: computational cost; functional equation; generalized Leibniz rule; Grünwald–Letnikov fractional derivative; Lerch zeta function