A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials
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Publication:5270793
DOI10.1177/1077546314543727zbMath1365.26005OpenAlexW1997453580MaRDI QIDQ5270793
Hassan Khosravian-Arab, Mehdi Dehghan, Ehsan-Allah Hamedi
Publication date: 3 July 2017
Published in: Journal of Vibration and Control (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1177/1077546314543727
Jacobi polynomialsCaputo derivativeRiemann-Liouville derivativefractional optimal control problemsfractional variational problems
Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Optimality conditions for problems involving relations other than differential equations (49K21)
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Uses Software
Cites Work
- Discrete direct methods in the fractional calculus of variations
- The construction of operational matrix of fractional derivatives using B-spline functions
- Discrete-time fractional variational problems
- A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations
- A numerical technique for solving fractional optimal control problems
- Calculus of variations with fractional derivatives and fractional integrals
- On a nonlinear distributed order fractional differential equation
- A new operational matrix for solving fractional-order differential equations
- Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- A formulation of Noether's theorem for fractional problems of the calculus of variations
- New applications of fractional variational principles
- Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
- Formulation of Euler-Lagrange equations for fractional variational problems
- Fractional sequential mechanics - models with symmetric fractional derivative.
- Application of the collocation method for solving nonlinear fractional integro-differential equations
- A general finite element formulation for fractional variational problems
- Numerical solution of a class of fractional optimal control problems via the Legendre orthonormal basis combined with the operational matrix and the Gauss quadrature rule
- On shifted Jacobi spectral approximations for solving fractional differential equations
- A general formulation and solution scheme for fractional optimal control problems
- The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems
- Fractional calculus of variations for a combined Caputo derivative
- A generalized fractional variational problem depending on indefinite integrals: Euler–Lagrange equation and numerical solution
- Fractional embedding of differential operators and Lagrangian systems
- Generalized Euler—Lagrange Equations and Transversality Conditions for FVPs in terms of the Caputo Derivative
- Nonconservative Lagrangian mechanics: a generalized function approach
- Stationarity$ndash$conservation laws for fractional differential equations with variable coefficients
- Extending Bauer's corollary to fractional derivatives
- General formulation for the numerical solution of optimal control problems
- On Computing the Points and Weights for Gauss--Legendre Quadrature
- Fractional variational calculus in terms of Riesz fractional derivatives
- Variational problems with fractional derivatives: Euler–Lagrange equations
- Nonholonomic constraints with fractional derivatives
- Fractional variational calculus and the transversality conditions
- The random walk's guide to anomalous diffusion: A fractional dynamics approach