Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1229

 Title: Cauchy Problem for Differential Equation with Caputo Derivative Authors: Kilbas, AnatolyMarzan, Sergei Keywords: Differential Equation of Fractional OrderCaputo DerivativeExistence and Uniqueness TheoremApproximate-Iterative Method34A1234B1526A3365L10 Issue Date: 2004 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Fractional Calculus and Applied Analysis, Vol. 7, No 3, (2004), 297p-321p Abstract: 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. URI: http://hdl.handle.net/10525/1229 ISSN: 1311-0454 Appears in Collections: 2004

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