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

Abstract

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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.

How to cite

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Kilbas, 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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