Browsing by Author "Alhamed, Yahia A."

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Citation Count: Baleanu, Dumitru...et al. (2014). "A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line", Abstract and Applied Analysis.
A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line
(Hindawi LTD, 2014) Bhrawy, A. H.; Alzahrani, Abdulrahim A.; Baleanu, Dumitru; Alhamed, Yahia A.; 56389
The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.
Fractional Sub-Equation Method For The Fractional Generalized Reaction Duffing Model and Nonlinear Fractional Sharma-Tasso-Olver Equation
(De Gruyter Poland SP Zoo, 2013) Jafari, Hossein; Tajadodi, Haleh; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; 56389
In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is described in the Jumarie's modified Riemann-Liouville sense. Two illustrative examples are given, showing the accuracy and convenience of the method.
Citation Count: Bhrawy, AH...et.al. (2014). "New spectral techniques for systems of fractional differential equations using fractional-order generalized laguerre orthogonal functions" Fractional Calculus and Applied Analysis, Vol.17, No.4, pp.1137-1157.
New spectral techniques for systems of fractional differential equations using fractional-order generalized laguerre orthogonal functions
(Walter De Gruyter GMBH, 2014) Bhrawy, A. H.; Alhamed, Yahia A.; Baleanu, Dumitru; Al-Zahrani, A. A.; 56389
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.
Citation Count: Nigmatullin, Raoul R...et al. (2013). "Spectral analysis of HIV drugs for acquired immunodeficiency syndrome within modified non-invasive methods", Revista de Chimie, Vol. 64, No. 9, pp. 987-993.
Spectral analysis of HIV drugs for acquired immunodeficiency syndrome within modified non-invasive methods
(2013) Nigmatullin, Raoul R.; Baleanu, Dumitru; Al-Zhrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; Youssef, Tamer L.; 56389
In this study a chromatographic separation of active ingredients for four drugs namely Combivir, Kaletra, Valcyte and Viramune was performed on thin layer chromatography (TLC). Their spectra were analyzed for acquired immunodeficiency syndrome by using the Fourier transform infrared spectroscopy spectra combined with the new procedure of the optimal linear smoothing. Fourier transform of the second type was applied as the Fitting function based on some significant set of frequencies for the smoothed signals. The obtained results show that the proposed method is efficient and easy to apply in extracting of a hidden information from signals corresponding to the four investigated drugs.