Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Diethelm, Kai

Fractional Calculus and Applied Analysis (2007)

  • Volume: 10, Issue: 2, page 151-160
  • ISSN: 1311-0454

Abstract

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Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.

How to cite

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Diethelm, Kai. "Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations." Fractional Calculus and Applied Analysis 10.2 (2007): 151-160. <http://eudml.org/doc/11324>.

@article{Diethelm2007,
abstract = {Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.},
author = {Diethelm, Kai},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 34A25; 45D05; 45E10},
language = {eng},
number = {2},
pages = {151-160},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations},
url = {http://eudml.org/doc/11324},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Diethelm, Kai
TI - Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 2
SP - 151
EP - 160
AB - Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.
LA - eng
KW - 26A33; 34A25; 45D05; 45E10
UR - http://eudml.org/doc/11324
ER -

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