Browsing by Author "Al-Zahrani, A. A."

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Citation Count: Bhrawy, A. H...et al. (2014). "A New Generalized Laguerre-Gauss Collocation Scheme For Numerical Solution Of Generalized Fractional Pantograph Equations", Romanian Journal of Physics, Vol. 59, No. 7-8, pp. 646-657.
A New Generalized Laguerre-Gauss Collocation Scheme For Numerical Solution Of Generalized Fractional Pantograph Equations
(2014) Bhrawy, A. H.; Al-Zahrani, A. A.; Alhamed, Y. A.; Baleanu, Dumitru; 56389
The manuscript is concerned with a generalization of the fractional pantograph equation which contains a linear functional argument. This type of equation has applications in many branches of physics and engineering. A new spectral collocation scheme is investigated to obtain a numerical solution of this equation with variable coefficients on a semi-infinite domain. This method is based upon the generalized Laguerre polynomials and Gauss quadrature integration. This scheme reduces solving the generalized fractional pantograph equation to a system of algebraic equations. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented.
Citation Count: Jafari, H...et al. (2013). "Exact solutions of Boussinesq and KdV-mKdV equations by fractional sub-equation method", Romanian Reports in Physics, Vol.65, No. 4, pp. 1119-1124.
Exact solutions of Boussinesq and KdV-mKdV equations by fractional sub-equation method
(2013) Jafari, H.; Tajadodi, H.; Baleanu, Dumitru; Al-Zahrani, A. A.; Alhamed, Y. A.; Zahid, A. H.; 56389
A fractional sub-equation method is introduced to solve fractional differential equations. By the aid of the solutions of the fractional Riccati equation, we construct solutions of the Boussinesq and KdV-mKdV equations of fractional order. The obtained results show that this method is very efficient and easy to apply for solving fractional partial differential equations.
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.