WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

Browse

Filters

2013 - 20206

Settings

COAR Access Rights: search.filters.coarAccessRights.open accessSubject: search.filters.subject.Operational Matrix

Search Results

Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 10
    Citation - Scopus: 8
    Derivation of Operational Matrix of Rabotnov Fractional-Exponential Kernel and Its Application To Fractional Lienard Equation
    (Elsevier, 2020) Gomez-Aguilar, J. F.; Lavin-Delgado, J. E.; Baleanu, D.; Kumar, Sachin
    Our motive in this contribution is to find out the operational matrix of fractional derivative having non singular kernel namely Rabotnov fractional-exponential (RFE) kernel which is recently introduced and seeking numerical solution of non-linear Lienard equation which have Rabotnov fractional-exponential kernel fractional derivative. First we derive an approximation formula of the fractional order derivative of polynomial function z(k) in term of RFE kernel. Using this formula and some properties of shifted Legendre polynomials, we find out the operational matrix of fractional order differentiation. In the author of knowledge this operational matrix of RFE kernel fractional derivative is derived first time. We solve a new class of fractional partial differential equation (FPDEs) by implementation of this newly derived operational matrix. We show that our newly derived operational matrix is valid by taking an fractional derivative of a polynomial. Also, we study a new model of Lienard equation with RFE kernel fractional derivative and we can easily predict the feasibility of our numerical method to this new model. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
  • Article
    Citation - WoS: 42
    Citation - Scopus: 56
    A Novel Jacobi Operational Matrix for Numerical Solution of Multi-Term Variable-Order Fractional Differential Equations
    (Taylor & Francis Ltd, 2020) Baleanu, D.; Agarwal, P.; El-Sayed, A. A.
    In this article, we introduce a numerical technique for solving a class of multi-term variable-order fractional differential equation.The method depends on establishing a shifted Jacobi operational matrix (SJOM) of fractional variable-order derivatives. By using the constructed (SJOM) in combination with the collocation technique, the main problem is reduced to an algebraic system of equations that can be solved numerically. The bound of the error estimate for the suggested method is investigated. Numerical examples are introduced to illustrate the applicability, generality, and accuracy of the proposed technique. Moreover, many physical applications problems that have the multi-term variable-order fractional differential equation formulae such as the damped mechanical oscillator problem and Bagley-Torvik equation can be solved via the presented method. Furthermore, the proposed method will be considered as a generalization of many numerical techniques.
  • Article
    Citation - WoS: 185
    Citation - Scopus: 202
    An Efficient Numerical Method for Fractional Sir Epidemic Model of Infectious Disease by Using Bernstein Wavelets
    (Mdpi, 2020) Ahmadian, Ali; Kumar, Ranbir; Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Salimi, Mehdi; Kumar, Sunil
    In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams-Bashforth-Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams-Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 45
    The 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: 96
    Citation - Scopus: 117
    A Jacobi Operational Matrix for Solving a Fuzzy Linear Fractional Differential Equation
    (Springer international Publishing Ag, 2013) Suleiman, Mohamed; Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali
    This paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order . A suitable representation of the fuzzy solution via Jacobi polynomials diminishes its numerical results to the solution of a system of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The efficiency and applicability of the proposed method are proved by several test examples.
  • Article
    Citation - WoS: 60
    Citation - Scopus: 64
    An Efficient Numerical Scheme Based on the Shifted Orthonormal Jacobi Polynomials for Solving Fractional Optimal Control Problems
    (Springeropen, 2015) Bhrawy, Ali H.; Baleanu, Dumitru; Ezz-Eldien, Samer S.; Hafez, Ramy M.; Doha, Eid H.
    In this article, we introduce a numerical technique for solving a general form of the fractional optimal control problem. Fractional derivatives are described in the Caputo sense. Using the properties of the shifted Jacobi orthonormal polynomials together with the operational matrix of fractional integrals (described in the Riemann-Liouville sense), we transform the fractional optimal control problem into an equivalent variational problem that can be reduced to a problem consisting of solving a system of algebraic equations by using the Legendre-Gauss quadrature formula with the Rayleigh-Ritz method. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.