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Title: Cauchy Problem for Differential Equation with Caputo Derivative
Authors: Kilbas, Anatoly
Marzan, Sergei
Keywords: Differential Equation of Fractional Order
Caputo Derivative
Existence and Uniqueness Theorem
Approximate-Iterative Method
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.
ISSN: 1311-0454
Appears in Collections:2004

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