Browsing by Author "Taha, Taha M."

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Citation Count: Bhrawy, Ali H...et.al. (2015). "New operational matrices for solving fractional differential equations on the half-line", Plos One, Vol.10, No.9, pp.1-23.
New operational matrices for solving fractional differential equations on the half-line
(Public Library Science, 2015) Bhrawy, Ali H.; Taha, Taha M.; Alzahrani, Ebraheem; Baleanu, Dumitru; Alzahrani, Abdulrahim A.; 56389
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.
Citation Count: Zaky, Mahmoud A...et al. (2018). "New Recursive Approximations for Variable-Order Fractional Operators with Applications", Mathematical Modelling and Analysis, Vol. 23, No. 2, pp. 227-239.
New Recursive Approximations for Variable-Order Fractional Operators with Applications
(Vilnius Gediminas Tech Univ, 2018) Zaky, Mahmoud A.; Doha, Eid H.; Taha, Taha M.; Baleanu, Dumitru; 56389
To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional initial value problems on the half line. Specifically, we derive three-term recurrence relations to efficiently calculate the variable-order fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.