WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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2015 - 20183

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Subject: search.filters.subject.Operational MatrixWoS Q: search.filters.wosQuartile.Q3

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 66
    Citation - Scopus: 63
    An Accurate Numerical Technique for Solving Fractional Optimal Control Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; Matematik
    In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 11
    Study on Application of Hybrid Functions To Fractional Differential Equations
    (Springer international Publishing Ag, 2018) Baleanu, D.; Torkzadeh, L.; Nouri, K.
    In this study we propose an efficient technique for approximate solution of linear and nonlinear differential equations with fractional order. The operational matrices based upon block-pulse functions and Chebyshev polynomials of the second kind are used for this purpose. Also, we focus on the upper bound of error for performance of the our estimates. The numerical results confirm the convergence of the suggested method. Correspondingly, the obtained results of our method are compared with other approaches in terms of efficiency and accuracy.
  • Article
    Citation - WoS: 49
    Citation - Scopus: 55
    Solving Fractional Optimal Control Problems Within a Chebyshev-Legendre Operational Technique
    (Taylor & Francis Ltd, 2017) Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.; Bhrawy, A. H.
    In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.