WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 97Citation - Scopus: 103New Spectral Techniques for Systems of Fractional Differential Equations Using Fractional-Order Generalized Laguerre Orthogonal Functions(Walter de Gruyter Gmbh, 2014) Alhamed, Yahia A.; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Bhrawy, Ali H.Fractional-order generalized Laguerre functions (FGLFs) are proposed depends on the definition of generalized Laguerre polynomials. In addition, we derive a new formula expressing explicitly any Caputo fractional-order derivatives of FGLFs in terms of FGLFs themselves. We also propose a fractional-order generalized Laguerre tau technique in conjunction with the derived fractional-order derivative formula of FGLFs for solving Caputo type fractional differential equations (FDEs) of order nu (0 < nu < 1). The fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order nu. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on FGLFs and compare them with other methods. Several numerical example are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.Article Citation - WoS: 13Citation - Scopus: 15New Operational Matrices for Solving Fractional Differential Equations on the Half-Line(Public Library Science, 2015) Taha, Taha M.; Alzahrani, Ebrahim O.; Baleanu, Dumitru; Alzahrani, Abdulrahim A.; Bhrawy, Ali H.In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order. (0 < v < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order.. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.Article Citation - WoS: 31Citation - Scopus: 35A Jacobi Gauss-Lobatto and Gauss-Radau Collocation Algorithm for Solving Fractional Fokker-Planck Equations(Springer, 2015) Ezz-Eldien, Samer S.; Bhrawy, Ali H.; Ahmed, Engy A.; Baleanu, Dumitru; Hafez, Ramy M.In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.