WoS İndeksli Yayınlar Koleksiyonu

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

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Subject: search.filters.subject.Local Fractional Variational Iteration Method

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Now showing 1 - 7 of 7
  • Article
    Citation - WoS: 52
    Citation - Scopus: 57
    Damped Wave Equation and Dissipative Wave Equation in Fractal Strings Within the Local Fractional Variational Iteration Method
    (Springer international Publishing Ag, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein; Su, Wei-Hua
    In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions. MSC: 74H10, 35L05, 28A80.
  • Article
    Citation - WoS: 239
    Citation - Scopus: 253
    Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method
    (Vinca inst Nuclear Sci, 2013) Baleanu, Dumitru; Yang, Xiao-Jun
    This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 51
    A Novel Approach for Korteweg-De Vries Equation of Fractional Order
    (Shahid Chamran Univ Ahvaz, Iran, 2019) Baleanu, Dumitru; Jassim, Hassan Kamil
    In this study, the local fractional variational iteration method (LFVIM) and the local fractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractional derivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very effective and simple and can be applied for linear and nonlinear problems in mathematical physics.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 60
    Solving Helmholtz Equation With Local Fractional Derivative Operators
    (Mdpi, 2019) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, Dumitru
    The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM), for solving the two-dimensional Helmholtz and coupled Helmholtz equations with local fractional derivative operators (LFDOs). The operators are taken in the local fractional sense. Two test problems are presented to demonstrate the efficiency and the accuracy of the proposed method. The approximate solutions obtained are compared with the results obtained by the local fractional Laplace decomposition method (LFLDM). The results reveal that the LFLVIM is very effective and convenient to solve linear and nonlinear PDEs.
  • Article
    Citation - WoS: 55
    Citation - Scopus: 84
    A Modification Fractional Variational Iteration Method for Solving Non-Linear Gas Dynamic and Coupled Kdv Equations Involving Local Fractional Operators
    (Vinca inst Nuclear Sci, 2018) Jassim, Hassan Kamil; Khan, Hasib; Baleanu, Dumitru
    In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 61
    On the Approximate Solutions of Local Fractional Differential Equations With Local Fractional Operators
    (Mdpi, 2016) Tchier, Fairouz; Baleanu, Dumitru; Jafari, Hossein; Jassim, Hassan Kamil
    In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
  • Conference Object
    Citation - WoS: 16
    Citation - Scopus: 15
    A 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.