Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 118Citation - Scopus: 132Novel Fractional-Order Lagrangian To Describe Motion of Beam on Nanowire(Polish Acad Sciences inst Physics, 2021) Godwe, E.; Erturk, V. S.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A.Our aim in this research is to investigate the motion of a beam on an internally bent nanowire by using the fractional calculus theory. To this end, we first formulate the classical Lagrangian which is followed by the classical Euler-Lagrange equation. Then, after introducing the generalized fractional Lagrangian, the fractional Euler-Lagrange equation is provided for the motion of the considered beam on the nanowire. An efficient numerical scheme is introduced for implementation and the simulation results are reported for different fractional-order values and various initial settings. These results indicate that the fractional responses approach the classical ones as the fractional order goes to unity. In addition, the fractional Euler-Lagrange equation provides a flexible model possessing more information than the classical description the fact that leads to a considerably better evaluation of the hidden features of the real system under investigation.Article Citation - WoS: 82Citation - Scopus: 86The Motion of a Bead Sliding on a Wire in Fractional Sense(Polish Acad Sciences inst Physics, 2017) Jajarmi, A.; Asad, J. H.; Blaszczyk, T.; Baleanu, D.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.Article Citation - WoS: 9Citation - Scopus: 10Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform(Polish Acad Sciences inst Physics, 2016) Blaszczyk, T.; Asad, J. H.; Alipour, M.; Baleanu, D.; Alipoure, M.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.