Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 94Citation - Scopus: 111A New and General Fractional Lagrangian Approach: A Capacitor Microphone Case(Elsevier, 2021) Baleanu, D.; Vahid, K. Zarghami; Pirouz, H. Mohammadi; Asad, J. H.; Jajarmi, A.; Mohammadi Pirouz, H.; Zarghami Vahid, K.In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler-Lagrange equations are constructed by using the classical Lagrangian approach. Expanding this classical scheme in a general fractional framework provides the new fractional Euler-Lagrange equations in which non-integer order derivatives involve a general function as their kernel. Applying an appropriate matrix approximation technique changes the latter fractional formulation into a nonlinear algebraic system. Finally, the derived system is solved numerically with a discussion on its dynamical behaviors. According to the obtained results, various features of the capacitor microphone under study are discovered due to the flexibility in choosing the kernel, unlike the previous mathematical formalism.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.