# On a Differential Equation with Left and Right Fractional Derivatives

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

top

## Abstract

top
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.

## How to cite

top

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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.