On a Differential Equation with Left and Right Fractional Derivatives

Atanackovic, 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 -