WoS İndeksli Yayınlar Koleksiyonu

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

Browse

Filters

2011 - 201952020 - 20211

Settings

Publisher: search.filters.publisher.Editura Acad RomaneSubject: search.filters.subject.Caputo Derivative

Search Results

Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 16
    Citation - Scopus: 23
    On Fractional Hamiltonian Systems Possessing First-Class Constraints Within Caputo Derivatives
    (Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Matematik
    The fractional constrained systems possessing only first class constraints are analyzed within Caputo fractional derivatives. It was proved that the fractional Hamilton-Jacobi like equations appear naturally in the process of finding the full canonical transformations. An illustrative example is analyzed.
  • Article
    Citation - WoS: 59
    Citation - Scopus: 66
    New Aspects of the Motion of a Particle in a Circular Cavity
    (Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; Matematik
    In this work, we consider the free motion of a particle in a circular cavity. For this model, we obtain the classical and fractional Lagrangian as well as the fractional Hamilton's equations (FHEs) of motion. The fractional equations are formulated in the sense of Caputo and a new fractional derivative with Mittag-Leffler nonsingular kernel. Numerical simulations of the FHEs within these two fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Simulation results show that the fractional calculus provides more flexible models demonstrating new aspects of the real-world phenomena.
  • Article
    Citation - WoS: 81
    Citation - Scopus: 94
    The Fractional Dynamics of a Linear Triatomic Molecule
    (Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; Matematik
    In this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 31
    A Novel Spectral Approximation for the Two-Dimensional Fractional Sub-Diffusion Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Zaky, M. A.; Baleanu, D.; Abdelkawy, M. A.; Matematik
    This paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.
  • Article
    Citation - WoS: 36
    A Lie Group Approach To Solve the Fractional Poisson Equation
    (Editura Acad Romane, 2015) Hashemi, M. S.; Baleanu, Dumitru; Baleanu, D.; Parto-Haghighi, M.; Matematik
    In the present paper, approximate solutions of fractional Poisson equation (FPE) have been considered using an integrator in the class of Lie groups, namely, the fictitious time integration method (FTIM). Based on the FTIM, the unknown dependent variable u(x, t) is transformed into a new variable with one more dimension. We use a fictitious time tau as the additional dimension (fictitious dimension), by transformation: v(x, t, tau) := (1 + tau)(k) u(x, t), where 0 < k <= 1 is a parameter to control the rate of convergency in the FTIM. Then the group preserving scheme (GPS) is used to integrate the new fractional partial differential equations in the augmented space R2+1. The power and the validity of the method are demonstrated using two examples.
  • Article
    Citation - WoS: 89
    Citation - Scopus: 124
    New Numerical Approximations for Space-Time Fractional Burgers' Equations Via a Legendre Spectral-Collocation Method
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Zaky, M. A.; Baleanu, D.
    Burgers' equation is a fundamental partial differential equation in fluid mechanics. This paper reports a new space-time spectral algorithm for obtaining an approximate solution for the space-time fractional Burgers' equation (FBE) based on spectral shifted Legendre collocation (SLC) method in combination with the shifted Legendre operational matrix of fractional derivatives. The fractional derivatives are described in the Caputo sense. We propose a spectral shifted Legendre collocation method in both temporal and spatial discretizations for the space-time FBE. The main characteristic behind this approach is that it reduces such problem to that of solving a system of nonlinear algebraic equations that can then be solved using Newton's iterative method. Numerical results with comparisons are given to confirm the reliability of the proposed method for FBE.