A Generalization of the Krätzel Function and Its Applications

Abstract

In this paper, we introduce new functions Yρ,r(x) as a generalization of the Krätzel function. We investigate recurrence relations, Mellin transform, fractional derivatives, and integral of the function Yρ,r(x). We show that the function Yρ,r(x) is the solution of differential equations of fractional order