WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Editorial Citation - WoS: 2Citation - Scopus: 3Fractional and Time-Scales Differential Equations(Hindawi Publishing Corporation, 2014) Torres, Delfim F. M.; Bhrawy, Ali H.; Salahshour, Soheil; Baleanu, DumitruArticle Citation - WoS: 5Citation - Scopus: 6A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line(Hindawi Ltd, 2014) AlZahrani, Abdulrahim; Baleanu, Dumitru; Alhamed, Yahia; Bhrawy, Ali H.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.Article Citation - WoS: 17Citation - Scopus: 16A Spectral Technique for Solving Two-Dimensional Fractional Integral Equations With Weakly Singular Kernel(Hacettepe Univ, Fac Sci, 2018) Abdelkawy, Mohamed A.; Baleanu, Dumitru; Amin, Ahmed Z. M.; Bhrawy, Ali H.; Amink, Ahmed Z. M.; Abdelkawyy, Mohamed A.This paper adapts a new numerical technique for solving twodimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equations. We apply the reported numerical method to solve several numerical examples in order to test the accuracy and validity. Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.Article Citation - WoS: 44Citation - Scopus: 52New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials(Springer/plenum Publishers, 2017) Hafez, Ramy M.; Bhrawy, Ali H.; Baleanu, Dumitru; El-Kalaawy, Ahmed A.; Ezz-Eldien, Samer S.This paper reports a new numerical approach for numerically solving types of fractional variational problems. In our approach, we use the fractional integrals operational matrix, described in the sense of Riemann-Liouville, with the help of the Lagrange multiplier technique for converting the fractional variational problem into an easier problem that consisting of solving an algebraic equations system in the unknown coefficients. Several numerical examples are introduced, combined with their approximate solutions and comparisons with other numerical approaches, for confirming the accuracy and applicability of the proposed approach.Conference Object Citation - WoS: 16Citation - Scopus: 15A New Numerical Technique for Solving Fractional Sub-Diffusion and Reaction Sub-Diffusion Equations With A Non-Linear Source Term(Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Mallawi, Fouad; Bhrawy, Ali H.In this paper, we are concerned with the fractional sub-diffusion equation with a non-linear source term. The Legendre spectral collocation method is introduced together with the operational matrix of fractional derivatives (described in the Caputo sense) to solve the fractional sub-diffusion equation with a non-linear source term. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. In addition, the Legendre spectral collocation methods applied also for a solution of the fractional reaction sub-diffusion equation with a non-linear source term. For confirming the validity and accuracy of the numerical scheme proposed, two numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.