A generalization of the Krätzel function and its applications (Q2421737)

Summary: In this paper, we introduce new functions \(Y_{\rho, r}^\nu(x)\) as a generalization of the Krätzel function. We investigate recurrence relations, Mellin transform, fractional derivatives, and integral of the function \(Y_{\rho, r}^\nu(x)\). We show that the function \(Y_{\rho, r}^\nu(x)\) is the solution of differential equations of fractional order.