Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Baleanu, D.Publisher: search.filters.publisher.Hindawi Ltd

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Now showing 1 - 10 of 19
  • Article
    Citation - WoS: 8
    Citation - Scopus: 35
    A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line
    (Hindawi Ltd, 2013) Baleanu, D.; Bhrawy, A. H.; Taha, T. M.
    This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomials L-i((alpha,beta)) (x) with x is an element of Lambda = (0, infinity), alpha > -1, and beta > 0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method
    (Hindawi Ltd, 2013) Alghamdi, M. A.; Baleanu, D.; Bhrawy, A. H.
    The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one-leg theta-method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 8
    Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems
    (Hindawi Ltd, 2013) Mohammadzadeh, B.; Neamaty, A.; Baleanu, D.; Darzi, R.; Bleanu, D.
    We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D(0+)(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, 2 < alpha <= 3, u(0) = u'(0) = 0, D-0(alpha-1),u(1) = beta u(xi), 0 < xi < 1, where D-0+(alpha) denotes Riemann-Liouville fractional derivative, beta is positive real number, beta xi(alpha-1) >= 2 Gamma(alpha), and f is continuous on [0, 1] x [0,infinity). As an application, one example is given to illustrate the main result.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Fractional Killing-Yano Tensors and Killing Vectors Using the Caputo Derivative in Some One- and Two-Dimensional Curved Space
    (Hindawi Ltd, 2014) Baleanu, D.; Malkawi, Ehab
    The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 28
    Variational Iteration Method for a Fractional-Order Brusselator System
    (Hindawi Ltd, 2014) Kadem, Abdelouahab; Baleanu, D.; Jafari, H.
    This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 10
    On Bernstein Polynomials Method To the System of Abel Integral Equations
    (Hindawi Ltd, 2014) Nia, S. Measoomy; Golmankhaneh, Alireza K.; Baleanu, D.; Jafarian, A.; Measoomy Nia, S.
    This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    Explicit Deconvolution of Well Test Data Dominated by Wellbore Storage
    (Hindawi Ltd, 2014) Hashemi, A.; Razminia, A.; Baleanu, D.; Razminia, K.
    This paper addresses some methods for interpretation of oil and gas well test data distorted by wellbore storage effects. Using these techniques, we can deconvolve pressure and rate data from drawdown and buildup tests dominated by wellbore storage. Some of these methods have the advantage of deconvolving the pressure data without rate measurement. The two important methods that are applied in this study are an explicit deconvolution method and a modification of material balance deconvolution method. In cases with no rate measurements, we use a blind deconvolution method to restore the pressure response free of wellbore storage effects. Our techniques detect the afterflow/unloading rate function with explicit deconvolution of the observed pressure data. The presented techniques can unveil the early time behavior of a reservoir system masked by wellbore storage effects and thus provide powerful tools to improve pressure transient test interpretation. Each method has been validated using both synthetic data and field cases and each method should be considered valid for practical applications.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 15
    Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators
    (Hindawi Ltd, 2014) Purohit, S. D.; Baleanu, D.
    By making use of the fractional hypergeometric operators, we establish certain new fractional integral inequalities for synchronous functions which are related to the weighted version of the Chebyshev functional. Some consequent results and special cases of the main results are also pointed out.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 4
    A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions
    (Hindawi Ltd, 2014) Baleanu, D.; Bhrawy, A. H.; Hafez, R. M.; Doha, E. H.
    A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational- Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational- Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 10
    A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations
    (Hindawi Ltd, 2013) Baleanu, D.; Bhrawy, A. H.; Abdelkawy, M. A.; Doha, E. H.
    We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters alpha and beta In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.