Scopus İndeksli Yayınlar Koleksiyonu

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

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Subject: search.filters.subject.Euler-Lagrange EquationWoS Q: search.filters.wosQuartile.Q1

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 86
    Citation - Scopus: 97
    On Fractional Derivatives With Generalized Mittag-Leffler Kernels
    (Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, Dumitru
    Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    A New Type of Equation of Motion and Numerical Method for a Harmonic Oscillator With Left and Right Fractional Derivatives
    (Elsevier, 2020) Baleanu, Dumitru; Ullah, Malik Zaka
    The aim of this research is to propose a new fractional Euler-Lagrange equation for a harmonic oscillator. The theoretical analysis is given in order to derive the equation of motion in a fractional framework. The new equation has a complicated structure involving the left and right fractional derivatives of Caputo-Fabrizio type, so a new numerical method is developed in order to solve the above-mentioned equation effectively. As a result, we can see different asymptotic behaviors according to the flexibility provided by the use of the fractional calculus approach, a fact which may be invisible when we use the classical Lagrangian technique. This capability helps us to better understand the complex dynamics associated with natural phenomena.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    On the Motion of a Heavy Bead Sliding on a Rotating Wire - Fractional Treatment
    (Elsevier, 2018) Asad, Jihad H.; Alipour, Mohsen; Baleanu, Dumitru
    In this work, we consider the motion of a heavy particle sliding on a rotating wire. The first step carried for this model is writing the classical and fractional Lagrangian. Secondly, the fractional Hamilton's equations (FHEs) of motion of the system is derived. The fractional equations are formulated in the sense of Caputo. Thirdly, numerical simulations of the FHEs within the 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. Finally, simulation results verify that, taking into account the fractional calculus provides more flexible models demonstrating new aspects of the real world phenomena.