# On a Differential Equation with Left and Right Fractional Derivatives

Atanackovic, Teodor; Stankovic, Bogoljub

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 2, page 139-150
- ISSN: 1311-0454

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topAtanackovic, Teodor, and Stankovic, Bogoljub. "On a Differential Equation with Left and Right Fractional Derivatives." Fractional Calculus and Applied Analysis 10.2 (2007): 139-150. <http://eudml.org/doc/11323>.

@article{Atanackovic2007,

abstract = {Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05We treat the fractional order differential equation that contains the left
and right Riemann-Liouville fractional derivatives. Such equations arise as
the Euler-Lagrange equation in variational principles with fractional derivatives.
We reduce the problem to a Fredholm integral equation and construct
a solution in the space of continuous functions. Two competing approaches
in formulating differential equations of fractional order in Mechanics and
Physics are compared in a specific example. It is concluded that only the
physical interpretation of the problem can give a clue which approach should
be taken.},

author = {Atanackovic, Teodor, Stankovic, Bogoljub},

journal = {Fractional Calculus and Applied Analysis},

keywords = {26A33; 70H03; 70S05; 49S05; 70H25},

language = {eng},

number = {2},

pages = {139-150},

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

title = {On a Differential Equation with Left and Right Fractional Derivatives},

url = {http://eudml.org/doc/11323},

volume = {10},

year = {2007},

}

TY - JOUR

AU - Atanackovic, Teodor

AU - Stankovic, Bogoljub

TI - On a Differential Equation with Left and Right Fractional Derivatives

JO - Fractional Calculus and Applied Analysis

PY - 2007

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 10

IS - 2

SP - 139

EP - 150

AB - Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05We treat the fractional order differential equation that contains the left
and right Riemann-Liouville fractional derivatives. Such equations arise as
the Euler-Lagrange equation in variational principles with fractional derivatives.
We reduce the problem to a Fredholm integral equation and construct
a solution in the space of continuous functions. Two competing approaches
in formulating differential equations of fractional order in Mechanics and
Physics are compared in a specific example. It is concluded that only the
physical interpretation of the problem can give a clue which approach should
be taken.

LA - eng

KW - 26A33; 70H03; 70S05; 49S05; 70H25

UR - http://eudml.org/doc/11323

ER -

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