Fractional variational calculus for nondifferentiable functions
arXiv:1103.5406 · doi:10.1016/j.camwa.2011.03.098
Abstract
We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints.
Submitted 13-Aug-2010; revised 24-Nov-2010; accepted 28-March-2011; for publication in Computers and Mathematics with Applications
References in corpus (15)
- Discrete-Time Fractional Variational Problems
- Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
- 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 Noether's theorem in the Riesz-Caputo sense
- 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
- Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems
- Isoperimetric problems on time scales with nabla derivatives
- Leitmann's direct method for fractional optimization problems
- The isoperimetric problem for Holderian curves
- Necessary and sufficient conditions for local Pareto optimality on time scales
- Composition Functionals in Fractional Calculus of Variations