A comprehensive review on fractional-order optimal control problem and its solution
From MaRDI portal
Publication:6611468
DOI10.1515/MATH-2023-0105zbMATH Open1548.49025MaRDI QIDQ6611468
Sayed M. Eldin, Shabir Ahmad, Rabha W. Ibrahim, Ramashis Banerjee, Mohamed R. Eid, Wasim Jamshed, K. S. Nisar, Assmaa Abd-Elmonem
Publication date: 26 September 2024
Published in: Open Mathematics (Search for Journal in Brave)
numerical methodstwo-point boundary value problemfractional order differential equationfractional delay differential equationfractional order optimal control problem
Boundary value problems for linear higher-order PDEs (35G15) Existence theories in calculus of variations and optimal control (49J99) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11) PDE constrained optimization (numerical aspects) (49M41)
Cites Work
- Approximate solution of multi-pantograph equation with variable coefficients
- Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\)
- Weighted average finite difference methods for fractional diffusion equations
- Tuning of PID controllers based on Bode's ideal transfer function
- A general formulation and solution scheme for fractional optimal control problems
- Approximations of fractional integrals and Caputo fractional derivatives
- The spectral method for solving systems of Volterra integral equations
- Numerical approximation of a one-dimensional space fractional advection-dispersion equation with boundary layer
- A new modification of Adomian decomposition method for solving a kind of evolution equation
- Finite difference methods for two-dimensional fractional dispersion equation
- Algorithms for the fractional calculus: a selection of numerical methods
- Finite difference approximations for two-sided space-fractional partial differential equations
- The operational matrix of integration for Bessel functions
- Chebyshev and Fourier spectral methods.
- Maximum principle for optimal control problem of stochastic delay differential equations driven by fractional Brownian motions
- An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index
- Fractional optimal control problems: a pseudo-state-space approach
- The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems
- Optimal Control Problem for Fractional Dynamic Systems – Linear Quadratic Discrete-Time Case
- A central difference numerical scheme for fractional optimal control problems
- A Bessel collocation method for numerical solution of generalized pantograph equations
- A collocation approach for solving linear complex differential equations in rectangular domains
- An Efficient Numerical Solution of Fractional Optimal Control Problems by using the Ritz Method and Bernstein Operational Matrix
- Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices
- Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation
- A Formulation and Numerical Scheme for Fractional Optimal Control Problems
- Fractional Multi-models of the Frog Gastrocnemius Muscle
- Modeling the Cardiac Tissue Electrode Interface Using Fractional Calculus
- Automatic Loop Shaping in QFT Using CRONE Structures
- Dynamic Measurements in Long-memory Materials: Fractional Calculus Evaluation of Approach to Steady State
- Design of Optimum Systems of Viscoelastic Vibration Absorbers for a Given Material Based on the Fractional Calculus Model
- The Fourier series operational matrix of integration
- A computational algorithm for large-scale nonlinear time-delay systems
- Numerical simulation for the 3D seepage flow with fractional derivatives in porous media
- Numerical approximations of fractional derivatives with applications
- A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems
- Fractional variational principles with delay
- Chebyshev polynomial approximation for high‐order partial differential equations with complicated conditions
- Hermite series approach to optimal control
- Systems with Time Delay in the Calculus of Variations: A Variational Approach
- Analysis and optimal control of time-varying linear systems via block-pulse functions
- Spectral Methods in MATLAB
- Optimal control of discrete-time linear fractional-order systems with multiplicative noise
- A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems
- An iterative approach for solving fractional optimal control problems
- Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- Solving fractional optimal control problems with fixed or free final states by Haar wavelet collocation method
- A numerical approximation for delay fractional optimal control problems based on the method of moments
- HOW TO APPROXIMATE THE FRACTIONAL DERIVATIVE OF ORDER 1 < α ≤ 2
- Book of Extremes
- Fractional Order PDαJoint Control of Legged Robots
- Numerical Methods for Fractional Differentiation
- A review and evaluation of numerical tools for fractional calculus and fractional order controls
- Solving fractional optimal control problems within a Chebyshev–Legendre operational technique
- Advances in Fractional Calculus
- Is Gauss Quadrature Better than Clenshaw–Curtis?
- Fractional variational calculus and the transversality conditions
- An Introduction to Delay Differential Equations with Applications to the Life Sciences
- Variational iteration method for autonomous ordinary differential systems
- The numerical solution of fractional differential equations: speed versus accuracy
- Analysis of fractional differential equations
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
- Some Ostrowski-Mercer Type Inequalities for Differentiable Convex Functions via Fractional Integral Operators with Strong Kernels
- On the fractional optimal control problems with a general derivative operator
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- An efficient numerical scheme based on the shifted orthonormal Jacobi polynomials for solving fractional optimal control problems
- A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differential-difference equations
- Fourier operational matrices of differentiation and transmission: introduction and applications
- A collocation method based on the Bernoulli operational matrix for solving high-order linear complex differential equations in a rectangular domain
- Fractional order optimal control problems with free terminal time
- Free final time fractional optimal control problems
- Higher order fractional variational optimal control problems with delayed arguments
- A numerical technique for solving a class of fractional variational problems
- On Riemann-Liouville and Caputo derivatives
- Numerical approaches to fractional calculus and fractional ordinary differential equation
- A collocation method using Hermite polynomials for approximate solution of pantograph equations
- Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term
- Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations
- Laguerre polynomial approach for solving linear delay difference equations
- Fractional optimal control problem of a distributed system in cylindrical coordinates
- Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
- A numerical technique for solving fractional optimal control problems
- A numerical approach for solving the high-order linear singular differential-difference equations
- On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
- State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems
- Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
- Recent history of fractional calculus
- Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
- Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid
- Optimal intervention strategy for prevention tuberculosis using a smoking-tuberculosis model
- A discrete method to solve fractional optimal control problems
- An approximate method for numerically solving multi-dimensional delay fractional optimal control problems by Bernstein polynomials
- A method for numerical integration on an automatic computer
- Fractional optimal control of a 2-dimensional distributed system using eigenfunctions
- Time-fractional radial diffusion in a sphere
- Stability analysis of linear fractional differential system with multiple time delays
- Fractional high order methods for the nonlinear fractional ordinary differential equation
- A second-order accurate numerical method for the two-dimensional fractional diffusion equation
- Variational iteration method -- a kind of non-linear analytical technique: Some examples
- Modified Adomian decomposition method for specific second order ordinary differential equations
- Remarks on fractional derivatives
- Integral fractional pseudospectral methods for solving fractional optimal control problems
- A mathematical model of dengue transmission with memory
- Rationalized Haar approach for nonlinear constrained optimal control problems
- Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
- Numerical algorithm based on Adomian decomposition for fractional differential equations
- On the fractional Adams method
- An approximate method for numerically solving fractional order optimal control problems of general form
- A note on the finite element method for the space-fractional advection diffusion equation
- Fractional-order systems and controls. Fundamentals and applications
- Computational algorithms for computing the fractional derivatives of functions
- Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
- On some explicit Adams multistep methods for fractional differential equations
- Analytical treatment and convergence of the Adomian decomposition method for a system of coupled damped wave equations
- Fractional derivatives in complex planes
- Fractional generalized splines and signal processing
- On the numerical evaluation of fractional derivatives in multi-degree-of-freedom systems
- Shifted Legendre direct method for variational problems
- The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
- Ordinary and delay differential equations
- Solving frontier problems of physics: the decomposition method
- An algorithm for the numerical solution of differential equations of fractional order
- Numerical solution of fractional order differential equations by extrapolation
- Recent applications of fractional calculus to science and engineering
- Numerical methods for the solution of partial differential equations of fractional order.
- A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
- Modeling diffusive transport with a fractional derivative without singular kernel
- On a new class of fractional operators
- A new approach for the nonlinear fractional optimal control problems with external persistent disturbances
- A pseudospectral method for fractional optimal control problems
- Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense
- Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach
- A new formulation of the fractional optimal control problems involving Mittag-Leffler nonsingular kernel
- A review of definitions for fractional derivatives and integral
- Wavelets method for solving fractional optimal control problems
- Fractional differential equations with a constant delay: stability and asymptotics of solutions
- A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- Variational iteration method for the Burgers' flow with fractional derivatives -- new Lagrange multipliers
- Detailed error analysis for a fractional Adams method
- Analysis of a system of fractional differential equations
- Chaos, fractional kinetics, and anomalous transport
- Waiting-times and returns in high-frequency financial data: An empirical study
- A predictor-corrector approach for the numerical solution of fractional differential equations
- Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators
- A new modification of the Adomian decomposition method for linear and nonlinear operators
- Finite difference approximations for fractional advection-dispersion flow equations
- Time-fractional radial diffusion in hollow geometries
- On a numerical scheme for solving differential equations of fractional order
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- Homotopy perturbation technique
- Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order
- Müntz-Legendre neural network construction for solving delay optimal control problems of fractional order with equality and inequality constraints
- Hermite-Jensen-Mercer type inequalities for Caputo fractional derivatives
- New aspects of time fractional optimal control problems within operators with nonsingular kernel
- A Bessel collocation method for solving fractional optimal control problems
- Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems
- Discrete-time fractional optimal control
- Short memory principle and a predictor-corrector approach for fractional differential equations
- A numerical method for delayed fractional-order differential equations
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems
- A new Legendre operational technique for delay fractional optimal control 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 the stable numerical evaluation of Caputo fractional derivatives
This page was built for publication: A comprehensive review on fractional-order optimal control problem and its solution
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6611468)
