Generalized Transversality Conditions in Fractional Calculus of Variations
arXiv:1207.5336 · doi:10.1016/j.cnsns.2012.07.009
Abstract
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the Bolza-type fractional variational problem, the fractional variational problem with a Lagrangian that may also depend on the unspecified end-point , where is a given curve, and the infinite horizon fractional variational problem.
This is a preprint of a paper whose final and definite form will be published in Communications in Nonlinear Science and Numerical Simulation, accepted 14-July-2012
References in corpus (15)
- Discrete-Time Fractional Variational Problems
- Fractional conservation laws in optimal control theory
- Calculus of variations with fractional derivatives and fractional integrals
- Fractional Hamilton formalism within Caputo's derivative
- Fractional Action-Like Variational Problems
- Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem
- Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order
- Noether's Theorem on Time Scales
- The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations
- Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
- Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
- Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
- Approximation of fractional integrals by means of derivatives
- Leitmann's direct method for fractional optimization problems