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Zbl 1177.26011
Kilbas, A.A.; Bonilla, B.; Trujillo, Juan J..
Fractional integrals and derivatives,and differential equations of fractional order in weighted spaces of continuous functions. (Russian. English summary)
[J] Dokl. Nats. Akad. Nauk Belarusi 44, No. 6, 18-22 (2000). ISSN 0002-354X

Summary: The properties of the Riemann-Liouville integrals and derivatives of any complex order 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 complex order and of the nonlinear Volterra integral equation. The existence and uniqueness of the solution of the above Cauchy-type problem is proved by using the method of successive approximations. The corresponding assertions for the Cauchy problem for ordinary differential equations are presented.

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
34A99 General theory of ODE
46N20 Appl. of functional analysis to differential and integral equations

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