Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method
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Publication:2018486
DOI10.1016/j.cam.2015.01.019zbMath1311.65087OpenAlexW2032428250MaRDI QIDQ2018486
Ahmed Alsaedi, Mohammad Maleki, Saeid Abbasbandy, Ishak Hashim
Publication date: 24 March 2015
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2015.01.019
convergencenumerical examplenonlinear programmingerror estimatecollocationEuler-Lagrange equationCaputo derivativefractional variational problemadaptive pseudospectral methodshifted Legendre-Gauss points
Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37) Existence theories for optimal control problems involving ordinary differential equations (49J15)
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Cites Work
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- Discrete direct methods in the fractional calculus of variations
- Approximation of fractional integrals by means of derivatives
- Fractional order optimal control problems with free terminal time
- Optimality conditions and a solution scheme for fractional optimal control problems
- Adaptive pseudospectral methods for solving constrained linear and nonlinear time-delay optimal control problems
- Fractional variational integrators for fractional variational problems
- Fractional calculus of variations in terms of a generalized fractional integral with applications to physics
- A numerical technique for solving a class of fractional variational problems
- Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
- Leitmann's direct method for fractional optimization problems
- Fractional Noether's theorem in the Riesz-Caputo sense
- The Hahn quantum variational calculus
- A unified framework for the numerical solution of optimal control problems using pseudospectral methods
- Generalized Euler-Lagrange equations for fractional variational problems with free boundary conditions
- Fractional variational problems depending on indefinite integrals
- Generalized variational calculus in terms of multi-parameters fractional derivatives
- Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
- Calculus of variations with fractional derivatives and fractional integrals
- Rationalized Haar approach for nonlinear constrained optimal control problems
- A numerical solution of problems in calculus of variation using direct method and nonclassical parameterization
- Generalized variational problems and Euler-Lagrange equations
- Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- Legendre-Gauss collocation methods for ordinary differential equations
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Pseudospectral Legendre-based optimal computation of nonlinear constrained variational problems
- Formulation of Euler-Lagrange equations for fractional variational problems
- Fractional sequential mechanics - models with symmetric fractional derivative.
- Fractional variational integrators for fractional Euler-Lagrange equations with holonomic constraints
- An adaptive pseudospectral method for fractional order boundary value problems
- A general finite element formulation for fractional variational problems
- Variational integrator for fractional Euler-Lagrange equations
- Pseudospectral methods based on nonclassical orthogonal polynomials for solving nonlinear variational problems
- Numerical approximations of fractional derivatives with applications
- Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative
- Stories about Maxima and Minima
- Spectral Methods in MATLAB
- A Global Convergence Analysis of an Algorithm for Large-Scale Nonlinear Optimization Problems
- An hp‐adaptive pseudospectral method for solving optimal control problems
- Variational problems with fractional derivatives: Euler–Lagrange equations
- Spectral Methods
- Mean convergence of orthogonal series and Lagrange interpolation
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