Scopus İndeksli Yayınlar Koleksiyonu

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

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Publisher: search.filters.publisher.de Gruyter Open Ltd

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Now showing 1 - 10 of 10
  • Book Part
    Citation - WoS: 1
    Citation - Scopus: 1
    Cantor-Type Spherical-Coordinate Method for Differential Equations Within Local Fractional Derivatives
    (de Gruyter Open Ltd, 2015) Rahmat, Mohamad Rah Segi; Baleanu, Dumitru; Yang, Xiao-Jun; Segi Rahmat, Mohamad Rafi
    In this article, we utilize the Cantor-type spherical coordinate method to investigate a family of local fractional differential operators on Cantor sets. Some examples are discussed to show the capability of this method for the damped wave, Helmholtz and heat conduction equations defined on Cantor sets. We show that it is a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type spherical-coordinate systems.
  • Book Part
    Numerical Solutions for Odes With Local Fractional Derivative
    (de Gruyter Open Ltd, 2015) Baleanu, Dumitru; Tenreiro Machado, J. A.; Yang, Xiao-Jun; Machado, J. A. Tenreiro
    In this chapter an efficient numerical algorithm for solving ODEs using the extended differential transform method via the generalized local fractional Taylor theorem is presented. Four examples are studied in order to illustrate the proposed technique.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 33
    Numerical Solutions of the Initial Value Problem for Fractional Differential Equations by Modification of the Adomian Decomposition Method
    (de Gruyter Open Ltd, 2014) Vaezpour, S. Mansour; Baleanu, Dumitru; Khodabakhshi, Neda; Mansour Vaezpour, S.
    In this paper, we extend a reliable modification of the Adomian decomposition method presented in [34] for solving initial value problem for fractional differential equations. In order to confirm the applicability and the advantages of our approach, we consider some illustrative examples.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 15
    On Combined Optical Solitons of the One-Dimensional Schrodinger's Equation With Time Dependent Coefficients
    (de Gruyter Open Ltd, 2016) Inc, Mustafa; Baleanu, Dumitru; Kilic, Bulent
    This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM) and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrodinger's equation (NLSE) with time dependent coefficients.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 20
    On Soliton Solutions of the Wu-Zhang System
    (de Gruyter Open Ltd, 2016) Kilic, Bulent; Karatas, Esra; Al Qurashi, Maysaa' Mohamed; Baleanu, Dumitru; Tchier, Fairouz; Inc, Mustafa; Mohamed Al Qurashi, Maysaa'
    In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ) system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 33
    Analysis of a New Fractional Model for Damped Bergers' Equation
    (de Gruyter Open Ltd, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev
    In this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.
  • Article
    Citation - WoS: 54
    Citation - Scopus: 55
    Non-Local Integrals and Derivatives on Fractal Sets With Applications
    (de Gruyter Open Ltd, 2016) Baleanu, D.; Golmankhaneh, Alireza K.
    In this paper, we discuss non-local derivatives on fractal Cantor sets. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared. Related physical models are also suggested.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 21
    On the Solutions of Electrohydrodynamic Flow With Fractional Differential Equations by Reproducing Kernel Method
    (de Gruyter Open Ltd, 2016) Baleanu, Dumitru; Inc, Mustafa; Tchier, Fairouz; Akgul, Ali
    In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 15
    Fixed Points for Cyclic Orbital Generalized Contractions on Complete Metric Spaces
    (de Gruyter Open Ltd, 2013) Tas, Kenan; Karapinar, Erdal; Romaguera, Salvador
    We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293-303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    Gravitational Potential in Fractional Space
    (de Gruyter Open Ltd, 2007) Baleanu, Dumitru; Rabei, Eqab M.; Muslih, Sami I.
    In this paper the gravitational potential with beta-th order fractional mass distribution was obtained in a dimensionally fractional space. We show that the fractional gravitational universal constant G(alpha) is given by G(alpha) = 2 Gamma(alpha/2)/Pi(alpha/2-1)(alpha-2) G, where G is the usual gravitational universal constant and the dimensionality of the space is alpha > 2. (c) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.