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Advanced Methods in the Fractional Calculus of Variations
SpringerBriefs in Applied Sciences and Technology, 2015 This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives.
Agnieszka B Malinowska +2 more
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Fractional Calculus of Variations
SpringerBriefs in Applied Sciences and Technology, 2015Agnieszka B Malinowska +2 more
exaly +2 more sources
A fractional calculus of variations for multiple integrals with application to vibrating string [PDF]
Journal of Mathematical Physics, 2010 We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of
Ricardo Almeida +2 more
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The Fractional Calculus of Variations
2018In this chapter, we consider general fractional problems of the calculus of variations, where the Lagrangian depends on a combined Caputo fractional derivative of variable fractional order \(^CD_\gamma ^{{\alpha (\cdot ,\cdot )},{\beta (\cdot ,\cdot )}}\) given as a combination of the left and the right Caputo fractional derivatives of orders ...
Ricardo Almeida +2 more
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Mediterranean Journal of MathematicsThrough duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators.
Delfim F M Torres, Torres Delfim F M
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Variational calculus with fractional action
Il Nuovo Cimento B, 2004The principle of the least fractional action δ{D - 1 - i / λ (Ψ(λ))} = 0 is constructed on Ω-space. This comes from the fact that the action is introduced as a form of entropy. Non-local behavior and breakdown of the causality in this space are reviewed. The deduction of Schrodinger's equation from this formalism is presented.
Gaies, A., Ziar, A.
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Multidimensional Discrete-Time Fractional Calculus of Variations
2015In this paper a discrete-time multidimensional fractional calculus of variations is introduced. The fractional operators are defined in the sense of Gr\(\ddot{u}\)nvald–Letnikov. We derive necessary optimality conditions and then give examples illustrating the use of obtained results.
Agnieszka B. Malinowska +1 more
openaire +1 more source