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New Operational Matrices for Solving Fractional Differential Equations on the Half-Line |
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| Authors: | Ali H. Bhrawy Taha M. Taha Ebrahim O. Alzahrani Dumitru Baleanu Abdulrahim A. Alzahrani |
| Affiliation: | 1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;3Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey;4Institute of Space Sciences, Magurele-Bucharest, Romania;Queensland University of Technology, AUSTRALIA |
| Abstract: | 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 ν (0 < ν < 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 ν. 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. |
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