On the solutions of some differential equations of fractional order in complex domain

The paper studies differential equations of fractional order of the form $D^{1/\rho}y(z)+\lambda y(z)=f(z)$ in the complex domain, where $\rho\geq 1, \ \lambda$ is an arbitrary parameter, $D^{1/\rho}$ is the Riemann–Liouville differential operator. For functions of some classes Cauchy type problems are considered.