Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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  • Article
    Citation - WoS: 68
    Citation - Scopus: 81
    Efficient Sustainable Algorithm for Numerical Solutions of Systems of Fractional Order Differential Equations by Haar Wavelet Collocation Method
    (Elsevier, 2020) Shah, Kamal; Al-Mdallal, Qasem; Jarad, Fahd; Abdeljawad, Thabet; Amin, Rohul
    This manuscript deals a numerical technique based on Haar wavelet collocation which is developed for the approximate solution of some systems of linear and nonlinear fractional order differential equations (FODEs). Based on these techniques, we find the numerical solution to var-ious systems of FODEs. We compare the obtain solution with the exact solution of the considered problems at integer orders. Also, we compute the maximum absolute error to demonstrate the effi-ciency and accuracy of the proposed method. For the illustration of our results we provide four test examples. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is defined in the Caputo sense. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
  • Article
    Citation - WoS: 20
    Citation - Scopus: 19
    A Highly Accurate Jacobi Collocation Algorithm for Systems of High-Order Linear Differential-Difference Equations With Mixed Initial Conditions
    (Wiley, 2015) Doha, E. H.; Baleanu, D.; Hafez, R. M.; Bhrawy, A. H.
    In this paper, a shifted Jacobi-Gauss collocation spectral algorithm is developed for solving numerically systems of high-order linear retarded and advanced differential-difference equations with variable coefficients subject to mixed initial conditions. The spatial collocation approximation is based upon the use of shifted Jacobi-Gauss interpolation nodes as collocation nodes. The system of differential-difference equations is reduced to a system of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The convergence is discussed graphically. The proposed method has an exponential convergence rate. The validity and effectiveness of the method are demonstrated by solving several numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. Copyright (C) 2015 John Wiley & Sons, Ltd.
  • Article
    Citation - WoS: 99
    Citation - Scopus: 110
    A New Jacobi Rational-Gauss Collocation Method for Numerical Solution of Generalized Pantograph Equations
    (Elsevier, 2014) Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.; Doha, E. H.
    This paper is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, a new spectral collocation method is applied to solve the generalized pantograph equation with variable coefficients on a semi-infinite domain. This method is based on Jacobi rational functions and Gauss quadrature integration. The Jacobi rational-Gauss method reduces solving the generalized pantograph equation to a system of algebraic equations. Reasonable numerical results are obtained by selecting few Jacobi rational-Gauss collocation points. The proposed Jacobi rational-Gauss method is favorably compared with other methods. Numerical results demonstrate its accuracy, efficiency, and versatility on the half-line. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 134
    Citation - Scopus: 154
    A New Approach for Solving Multi Variable Orders Differential Equations With Mittag-Leffler Kernel
    (Pergamon-elsevier Science Ltd, 2020) Jafari, H.; Baleanu, D.; Ganji, R. M.
    In this paper we consider multi variable orders differential equations (MVODEs) with non-local and no-singular kernel. The derivative is described in Atangana and Baleanu sense of variable order. We use the fifth-kind Chebyshev polynomials as basic functions to obtain operational matrices. We transfer the original equations to a system of algebraic equations using operational matrices and collocation method. The convergence analysis of the presented method is discussed. Few examples are presented to show the efficiency of the presented method. (C) 2019 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order
    (Edp Sciences S A, 2018) Darzi, Rahmat; Agheli, Ahram; Baleanu, Dumitru; Agheli, Bahram
    It is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) D-upsilon y(t) + eta integral(t)(0) (t - s)(zeta-1) y(s) ds = g(t), 1 < upsilon <= 2, 0 < zeta < 1, eta is an element of R, where D-upsilon denotes the Caputo derivative of order upsilon. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.
  • Article
    Citation - WoS: 138
    Citation - Scopus: 147
    Thermal and Velocity Slip Effects on Casson Nanofluid Flow Over an Inclined Permeable Stretching Cylinder Via Collocation Method
    (Pergamon-elsevier Science Ltd, 2018) Soomro, Feroz Ahmed; Haq, Rizwan Ul; Wang, W.; Defterli, Ozlem; Usman, M.; Ul Haq, Rizwan
    The main emphasis of present work is to investigate the velocity and thermal slip effects on Casson nano fluid with heat and mass transfer phenomena over an inclined permeable stretching cylinder. The cylinder is subject to transverse magnetic field. Buongiorno's model is adapted to study the Brownian motion and thermphoresis effects which play a dominant role in nanofluid. Governing set of equations are derived in terms of partial differential equations for Casson nanofluid model, consisting continuity, momentum, energy and concentration equation which are transformed into set of coupled nonlinear ordinary differential equations using similarity transformation. The numerical solution is obtained using collocation method. The literature survey shows that the present problem has not been studied before. Physical quantities of interest are nanofluid velocity, temperature, concentration, skin friction coefficient, Nusselt number and Sherwood number which are analyzed through graphs against the emerging physical parameters. It is found that Nb and Nt play a dominant role within the thermal and concentration boundary layer regions. In the same manner, suction parameter and both velocity and thermal slip parameters depicts the dynamic effects in the entire domain of stretching surface of the cylinder. (C) 2018 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 50
    Citation - Scopus: 64
    New Studies for General Fractional Financial Models of Awareness and Trial Advertising Decisions
    (Pergamon-elsevier Science Ltd, 2017) Abou Hasan, Muner M.; Baleanu, Dumitru; Sweilam, Nasser H.
    In this paper, two numerical techniques are introduced to study numerically the general fractional advertising model. This system describes the flux of the consumers from unaware individuals group to aware or purchased group. The first technique is an asymptotically stable difference scheme, which was structured depending on the nonstandard finite difference method. This scheme preserves the properties of the solutions of the model problem as the positivity and the boundedness. The second technique is the Jacobi-Gauss-Lobatto spectral collocation method which is exponentially accurate. By means of this approach, such problem is reduced to solve a system of nonlinear algebraic equations and are greatly simplified the problem. Numerical comparisons to test the behavior of the used techniques are run out. We conclude from the computational work that: the Jacobi-Gauss-Lobatto spectral collocation method is more accurate whereas the nonstandard finite difference method requires less computational time. (C) 2017 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 35
    A Jacobi Gauss-Lobatto and Gauss-Radau Collocation Algorithm for Solving Fractional Fokker-Planck Equations
    (Springer, 2015) Ezz-Eldien, Samer S.; Bhrawy, Ali H.; Ahmed, Engy A.; Baleanu, Dumitru; Hafez, Ramy M.
    In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.