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, TeodorStankovic, Bogoljub Keywords: Left and Right Riemann-Liouville Fractional DerivativesFractional Differential EquationEuler-Lagrange EquationVariational Principle26A3370H0370S0549S0570H25 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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