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Zbl 1114.34005
Kilbas, Anatoly A.; Marzan, Sergei A.
Cauchy problem for differential equation with Caputo derivative. (English)
[J] Fract. Calc. Appl. Anal. 7, No. 3, 297-321 (2004). ISSN 1311-0454; ISSN 1314-2224/e

Summary: The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

MSC 2000:: *34A12 Initial value problems for ODE
34B15 Nonlinear boundary value problems of ODE
26A33 Fractional derivatives and integrals (real functions)
65L10 Boundary value problems for ODE (numerical methods)

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