A Generalization of the Krätzel Function and Its Applications

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