# Cauchy Problem for Differential Equation with Caputo Derivative

Kilbas, Anatoly; Marzan, Sergei

Fractional Calculus and Applied Analysis (2004)

- Volume: 7, Issue: 3, page 297-321
- ISSN: 1311-0454

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topKilbas, Anatoly, and Marzan, Sergei. "Cauchy Problem for Differential Equation with Caputo Derivative." Fractional Calculus and Applied Analysis 7.3 (2004): 297-321. <http://eudml.org/doc/11247>.

@article{Kilbas2004,

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.},

author = {Kilbas, Anatoly, Marzan, Sergei},

journal = {Fractional Calculus and Applied Analysis},

keywords = {34A12; 34B15; 26A33; 65L10},

language = {eng},

number = {3},

pages = {297-321},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Cauchy Problem for Differential Equation with Caputo Derivative},

url = {http://eudml.org/doc/11247},

volume = {7},

year = {2004},

}

TY - JOUR

AU - Kilbas, Anatoly

AU - Marzan, Sergei

TI - Cauchy Problem for Differential Equation with Caputo Derivative

JO - Fractional Calculus and Applied Analysis

PY - 2004

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 7

IS - 3

SP - 297

EP - 321

AB - 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.

LA - eng

KW - 34A12; 34B15; 26A33; 65L10

UR - http://eudml.org/doc/11247

ER -

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