Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Baleanu, D.Publisher: search.filters.publisher.Sage Publications Ltd

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 40
    Citation - Scopus: 53
    Efficient Generalized Laguerre-Spectral Methods for Solving Multi-Term Fractional Differential Equations on the Half Line
    (Sage Publications Ltd, 2014) Baleanu, D.; Assas, L. M.; Bhrawy, A. H.
    The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) on the half line with constant coefficients using a generalized Laguerre tau (GLT) method. The fractional derivatives are described in the Caputo sense. We state and prove a new formula expressing explicitly the derivatives of generalized Laguerre polynomials of any degree and for any fractional order in terms of generalized Laguerre polynomials themselves. We develop also a direct solution technique for solving the linear multi-order FDEs with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives described in the Caputo sense are based on generalized Laguerre polynomials L-i((alpha))(x) with x is an element of Lambda = (0,infinity) and i denoting the polynomial degree.
  • Article
    Citation - WoS: 111
    Citation - Scopus: 122
    A Hybrid Functions Numerical Scheme for Fractional Optimal Control Problems: Application To Nonanalytic Dynamic Systems
    (Sage Publications Ltd, 2018) Moradi, L.; Baleanu, D.; Jajarmi, A.; Mohammadi, F.
    In this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs). To this end, by using the orthogonal Chelyshkov polynomials, the HCFs are constructed and a general formulation for their operational matrix of the fractional integration, in the Riemann-Liouville sense, is derived. This operational matrix together with HCFs are used to reduce the FOCP to a system of algebraic equations, which can be solved by any standard iterative algorithm. Moreover, the application of presented method to the problems with a nonanalytic dynamic system is investigated. Numerical results confirm that the proposed HCFs method can achieve spectral accuracy to approximate the solution of FOCPs.
  • Article
    Citation - WoS: 64
    Citation - Scopus: 69
    A Direct Numerical Solution of Time-Delay Fractional Optimal Control Problems by Using Chelyshkov Wavelets
    (Sage Publications Ltd, 2019) Mohammadi, F.; Baleanu, D.; Moradi, L.
    The aim of the present study is to present a numerical algorithm for solving time-delay fractional optimal control problems (TDFOCPs). First, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet functions and their properties are implemented to derive some operational matrices. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by means of the Chelyshkov wavelets. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algebraic system. Moreover, some illustrative examples are considered and the obtained numerical results were compared with those previously published in the literature.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 40
    Shifted Chebyshev Schemes for Solving Fractional Optimal Control Problems
    (Sage Publications Ltd, 2019) Moussa, H.; Baleanu, D.; El-Kady, M.; Abdelhakem, M.
    Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 82
    A Numerical Approach Based on Legendre Orthonormal Polynomials for Numerical Solutions of Fractional Optimal Control Problems
    (Sage Publications Ltd, 2017) Doha, E. H.; Baleanu, D.; Bhrawy, A. H.; Ezz-Eldien, S. S.
    The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.