Calculus of variations with fractional derivatives and fractional integrals
arXiv:0907.1024 · doi:10.1016/j.aml.2009.07.002
Abstract
We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Accepted (July 6, 2009) for publication in Applied Mathematics Letters
References in corpus (5)
- A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
- Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
- Fractional conservation laws in optimal control theory
- Fractional Hamilton formalism within Caputo's derivative
- Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order
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- Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
- Duality for the left and right fractional derivatives
- Fractional variational calculus for nondifferentiable functions
- Leitmann's direct method for fractional optimization problems
- Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order
- Composition Functionals in Fractional Calculus of Variations
- Fractional Calculus on Time Scales
- Minimal modified energy control for fractional linear control systems with the Caputo derivative
- Existence and Uniqueness of Solution to a Functional Integro-differential Fractional Equation
- Fractional Calculus of Variations for Double Integrals
- A variational approach to the analysis of non-conservative mechatronic systems