Browsing by Author "Asad, J. H."

Now showing 1 - 6 of 6

Citation - WoS: 68
Citation - Scopus: 70
Classical and Fractional Aspects of Two Coupled Pendulums
(Editura Acad Romane, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Asad, J. H.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.
Citation - WoS: 25
Citation - Scopus: 27
Fractional Euler-Lagrange Equation of Caldirola-Kanai Oscillator
(Editura Acad Romane, 2012) Baleanu, D.; Baleanu, Dumitru; Asad, J. H.; Petras, I.; Elagan, S.; Bilgen, A.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A study of the fractional Lagrangian of the so-called Caldirola-Kanai oscillator is presented. The fractional Euler-Lagrangian equations of the system have been obtained, and the obtained Euler-Lagrangian equations have been studied numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.
Citation - WoS: 79
Citation - Scopus: 82
The 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.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 1
Citation - Scopus: 2
Motion of a Spherical Particle in a Rotating Parabola Using Fractional Lagrangian
(Univ Politehnica Bucharest, Sci Bull, 2017) Baleanu, D.; Baleanu, Dumitru; Asad, J. H.; Alipour, M.; Blaszczyk, T.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 92
Citation - Scopus: 110
A 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.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 9
Citation - Scopus: 10
Numerical 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.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.