Browsing by Author "Blaszczyk, Tomasz"

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Citation Count: Baleanu, Dumitru...et al. (2017). "Motion Of A Spherical Particle In A Rotating Parabola Using Fractional Lagrangian", University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, Vol. 79, No: 2, pp. 183-192.
Motion Of A Spherical Particle In A Rotating Parabola Using Fractional Lagrangian
(Univ Politehnica Bucharest, 2017) Baleanu, Dumitru; Asad, Jihad H.; Alipour, Mohsen; Blaszczyk, Tomasz; 56389
In this work, the fractional Lagrangian of a particle moving in a rotating parabola is used to obtain the fractional Euler- Lagrange equations of motion where derivatives within it are given in Caputo fractional derivative. The obtained fractional Euler- Lagrange equations are solved numerically by applying the Bernstein operational matrices with Tau method. The results obtained are very good and when the order of derivative closes to 1, they are in good agreement with those obtained in Ref. [10] using Multi step- Differential Transformation Method (Ms-DTM).
Citation Count: Baleanu, D...et al. 2016). Numerical study for fractional euler-lagrange equations of a harmonic oscillator on a moving platform. Acta Physica Polonica A, 130(3), 688-691. http://dx.doi.org/ 10.12693/APhysPolA.130.688
Numerical study for fractional euler-lagrange equations of a harmonic oscillator on a moving platform
(Polish Acad Sciences Inst Physics, 2016) Baleanu, Dumitru; Blaszczyk, Tomasz; Asad, Jihad H.; Alipour, Mohsen
We investigate the fractional harmonic oscillator on a moving platform. We obtained the fractional Euler-Lagrange equation from the derived fractional Lagrangian of the system which contains left Caputo fractional derivative. We transform the obtained differential equation of motion into a corresponding integral one and then we solve it numerically. Finally, we present many numerical simulations.
Citation Count: Baleanu, D...et al. (2017). The Motion of a Bead Sliding on a Wire in Fractional Sense, Acta Physica Polonica A, 131(6), 561-1564.
The Motion of a Bead Sliding on a Wire in Fractional Sense
(Polish Acad Sciences Inst Physics, 2017) Baleanu, Dumitru; Jajarmi, Amin; Asad, Jihad H.; Blaszczyk, Tomasz; 56389
In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grunwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.