Kilbas, A. A.; Knyazyuk, N. V. Fractional integrals and derivatives on the half-axis and differential equations of fractional order in weighted spaces of continuous functions. (Russian. English summary) Zbl 1260.34146 Dokl. Nats. Akad. Nauk Belarusi 51, No. 6, 10-16 (2007). Summary: The properties of fractional integrals and derivatives of any positive order on the half-axis are investigated in weighted spaces of continuous functions. The results obtained are applied to prove the equivalence of the Cauchy-type problem for the nonlinear differential equation of fractional order and of the nonlinear Volterra integral equations. The existence and uniqueness of the solution of the above Cauchy-type problem is proved using the Banach fixed point theorem. The corresponding assertions for the Cauchy problem for the ordinary differential equation are presented. MSC: 34K37 Functional-differential equations with fractional derivatives 26A33 Fractional derivatives and integrals PDFBibTeX XMLCite \textit{A. A. Kilbas} and \textit{N. V. Knyazyuk}, Dokl. Nats. Akad. Nauk Belarusi 51, No. 6, 10--16 (2007; Zbl 1260.34146)