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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1312

Title: On a Differential Equation with Left and Right Fractional Derivatives
Authors: Atanackovic, Teodor
Stankovic, Bogoljub
Keywords: Left and Right Riemann-Liouville Fractional Derivatives
Fractional Differential Equation
Euler-Lagrange Equation
Variational Principle
26A33
70H03
70S05
49S05
70H25
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 2, (2007), 139p-150p
Abstract: We 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.
Description: Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05
URI: http://hdl.handle.net/10525/1312
ISSN: 1311-0454
Appears in Collections:2007

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