The Laplace‐collocation method for solving fractional differential equations and a class of fractional optimal control problems

Rakhshan, Seyed Ali; Effati, Sohrab

doi:10.1002/oca.2399

Cited by 12 publications

(2 citation statements)

References 35 publications

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“…Tohidi and Saberi 19 used the collocation method to solve the FOCP using the truncated Bessel series approximation. Similarly, Rakhshan and Effati 20 solve FOCP in the Caputo sense using Laplace transforms and the Chebyshev–Gauss collocation method. Some scientific studies on fractional order optimal control problems have been proposed in previous studies 21–25 .…”

Section: Introductionmentioning

confidence: 99%

Fractional optimal reachability problems withψ‐Hilfer fractional derivative

Vellappandi¹,

Govindaraj²,

Sousa

2022

Math Methods in App Sciences

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The aim of this article is to investigate the optimal reachability problem in terms of the 𝜓-Hilfer fractional derivative for a fractional dynamical system.Euler-Lagrange equations are used to obtain the necessary optimality constraints for the fractional optimal reachability problem (FORP). In terms of the 𝜓-Hilfer fractional derivative, we developed the predictor-corrector algorithm to provide numerical solutions to the FORP. Three numerical examples are provided to show the correctness of theoretical outputs.

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Section: Introductionmentioning

confidence: 99%

Fractional optimal reachability problems withψ‐Hilfer fractional derivative

Vellappandi¹,

Govindaraj²,

Sousa

2022

Math Methods in App Sciences

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“…Some efficient numerical methods for solving fractional differential equations involving delay have been developed in References 10‐17. Several numerical techniques regarding fractional optimal control problems without delay can be found in References 18‐28. Also, some direct methods for solving linear fractional optimal control problems including delay were given in References 29‐33.…”

Section: Introductionmentioning

confidence: 99%

Solution of a specific class of nonlinear fractional optimal control problems including multiple delays

Marzban

2020

Optim Control Appl Methods

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SummaryThis research provides a new framework based on a hybrid of block‐pulse functions and Legendre polynomials for the numerical examination of a special class of scalar nonlinear fractional optimal control problems involving delay. The concepts of the fractional derivative and the fractional integral are employed in the Caputo sense and the Riemann‐Liouville sense, respectively. In accordance with the notion of the Riemann‐Liouville integral, we derive a new integral operator related to the proposed basis called the operational matrix of fractional integration. By employing two significant operators, namely, the delay operator and the integral operator connected to the hybrid basis, the system dynamics of the primal optimal control problem converts to another system involving algebraic equations. Consequently, the optimal control problem under study is reduced to a static optimization one that is solved by existing well‐established optimization procedures. Some new theoretical results regarding the new basis are obtained. Various kinds of fractional optimal control problems containing delay are examined to measure the accuracy of the new method. The simulation results justify the merits and superiority of the devised procedure over the existing optimization methods in the literature.

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Convergence and stability of spectral collocation method for hyperbolic partial differential equation with piecewise continuous arguments

Chen

Wang

2022

Comp. Appl. Math.

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The Laplace‐collocation method for solving fractional differential equations and a class of fractional optimal control problems

Cited by 12 publications

References 35 publications

Fractional optimal reachability problems withψ‐Hilfer fractional derivative

Fractional optimal reachability problems withψ‐Hilfer fractional derivative

Solution of a specific class of nonlinear fractional optimal control problems including multiple delays

Convergence and stability of spectral collocation method for hyperbolic partial differential equation with piecewise continuous arguments

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