WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 29Citation - Scopus: 31A Novel Spectral Approximation for the Two-Dimensional Fractional Sub-Diffusion Problems(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Zaky, M. A.; Baleanu, D.; Abdelkawy, M. A.; MatematikThis paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.Article Citation - WoS: 3Citation - Scopus: 3Numerical Solution of Space-Time Variable Fractional Order Advection-Dispersion Equation Using Jacobi Spectral Collocation Method(Univ Putra Malaysia Press, 2020) Moghadam, Soltanpour A.; Baleanu, Dumitru; Arabameri, M.; Barfeie, M.; Baleanu, D.; Soltanpour Moghadam, A.; MatematikThis article is aimed at studying computational solution of variable order fractional advection-dispersion equation for one-dimensional and two-dimensional spaces utilizing spectral collocation method. In the considered model, the time derivative is Coimbra fractional derivative and space derivative is a Riemann-Liouville derivative. Jacobi polynomials are applied as basic functions in approximation of the solution. The presented approach is an application of the shifted Jacobi-Gauss collocation (SJ-G-C) and the shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods using for discretizing along space and time, respectively. Using the related collocation points, the problem would be changed to an algebraic equation system, which can be tackled applying a computational technique. At the end, several examples in one and two dimensional cases have been solved by introduced approach, it would be shown that the proposed numerical algorithm has considerably higher accuracy in contrast to the existing computational schemes including finite difference approach.Article Citation - WoS: 13Citation - Scopus: 16A Robust Scheme for Caputo Variable-Order Time-Fractional Diffusion-Type Equations(Springer, 2023) Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Hincal, Evren; Sadri, KhadijehThe focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling scientific phenomena in the context of fluid flow problems, curing reactions of thermosetting systems, solid oxide fuel cells, and solvent diffusion into heavy oils led to the appearance of these equations. For this reason, the numerical solution of these equations has attracted a lot of attention. More precisely, using pseudo-operational matrices and appropriate approximations based on bivariate Jacobi polynomials, the approximate solutions of the variable-order time-fractional diffusion-type equations in the Caputo sense with high accuracy are formally retrieved. Based on orthogonal bivariate Jacobi polynomials and their operational matrices, a sparse algebraic system is generated which makes implementing the proposed approach easy. An error bound is computed for the residual function by proving some theorems. To illustrate the accuracy and efficiency of the scheme, several illustrative examples are considered. The results demonstrate the efficiency of the present method compared to those achieved by the Legendre and Lucas multi-wavelet methods and the Crank-Nicolson compact method.Article Citation - WoS: 37Citation - Scopus: 45The Operational Matrix Formulation of the Jacobi Tau Approximation for Space Fractional Diffusion Equation(Springer, 2014) Bhrawy, Ali H.; Baleanu, Dumitru; Ezz-Eldien, Samer S.; Doha, Eid H.In this article, an accurate and efficient numerical method is presented for solving the space-fractional order diffusion equation (SFDE). Jacobi polynomials are used to approximate the solution of the equation as a base of the tau spectral method which is based on the Jacobi operational matrices of fractional derivative and integration. The main advantage of this method is based upon reducing the nonlinear partial differential equation into a system of algebraic equations in the expansion coefficient of the solution. In order to test the accuracy and efficiency of our method, the solutions of the examples presented are introduced in the form of tables to make a comparison with those obtained by other methods and with the exact solutions easy.Article Citation - WoS: 24Citation - Scopus: 22Shifted Jacobi Spectral Collocation Method With Convergence Analysis for Solving Integro-Differential Equations and System of Integro-Differential Equations(inst Mathematics & informatics, 2019) Abdelkawy, Mohamed A.; Amin, Ahmed Z. M.; Baleanu, Dumitru; Doha, Eid H.This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE.