Displaying similar documents to “lnfinitely many solutions for fractional Schrödinger equations with perturbation via variational methods”

Calculus of Variations with Classical and Fractional Derivatives

Odzijewicz, Tatiana, Torres, Delfim F. M. (2012)

Mathematica Balkanica New Series

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MSC 2010: 49K05, 26A33 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.

Hamilton’s Principle with Variable Order Fractional Derivatives

Atanackovic, Teodor, Pilipovic, Stevan (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined...

On a Differential Equation with Left and Right Fractional Derivatives

Atanackovic, Teodor, Stankovic, Bogoljub (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 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...

Fractional derivative generalization of Noether’s theorem

Maryam Khorshidi, Mehdi Nadjafikhah, Hossein Jafari (2015)

Open Mathematics

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The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an application of the theory.