Browsing by Author "Asad, Jihad H."

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Citation Count: Jajarmi, A...et al. (2017). "A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach", Frontiers in Physics, Vol. 7.
A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach
(Frontiers Media S.A., 2019) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, S. S.; Asad, Jihad H.; 56389
In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler–Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler–Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag–Leffler non-singular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modeling. Finally, we report our numerical findings to verify the theoretical analysis. © Copyright © 2019 Jajarmi, Baleanu, Sajjadi and Asad.
Citation Count: Baleanu, D.; Jajarmi, A.; Asad, J. H., "Classical and Fractional Aspects of Two Coupled Pendulums", Vol. 71, No. 1, (2019).
Classical and Fractional Aspects of Two Coupled Pendulums
(Editura Academiei Romane, 2019) Baleanu, Dumitru; Jajarmi, Amin; Asad, Jihad H.; 56389
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 Count: Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo, "Fractional Bateman-Feshbach Tikochinsky Oscillator", Communications in Theoretical Physics, 61, No. 2, pp. 221-225, (2014).
Fractional Bateman-Feshbach Tikochinsky Oscillator
(IOP Publishing LTD, 2014) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; 56389
In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman-Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grunwald-Letnikov approach, which is power series expansion of the generating function.
Citation Count: Baleanu, D...et al. (2012). "FRACTIONAL EULER-LAGRANGE EQUATION OF CALDIROLA-KANAI OSCILLATOR, Romanian Reports In Physics, Vol. 64, pp. 1171-1177.
Fractional Euler-Lagrange Equation of Caldirola-Kanai Oscillator
(Editura Academiei Romane, 2012) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; Elagan, S.; Bilgen, A.; 56389
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 Count: Baleanu, D...et.al. (2023). "Fractional investigation of time-dependent mass pendulum", Journal of Low Frequency Noise Vibration and Active Control.
Fractional investigation of time-dependent mass pendulum
(2023) Baleanu, Dumitru; Jajarmi, Amin; Defterli, Özlem; Wannan, Rania; Sajjadi, Samaneh S; Asad, Jihad H.; 56389; 31401
In this paper, we aim to study the dynamical behaviour of the motion for a simple pendulum with a mass decreasing exponentially in time. To examine this interesting system, we firstly obtain the classical Lagrangian and the Euler-Lagrange equation of the motion accordingly. Later, the generalized Lagrangian is constructed via non-integer order derivative operators. The corresponding non-integer Euler-Lagrange equation is derived, and the calculated approximate results are simulated with respect to different non-integer orders. Simulation results show that the motion of the pendulum with time-dependent mass exhibits interesting dynamical behaviours, such as oscillatory and non-oscillatory motions, and the nature of the motion depends on the order of non-integer derivative; they also demonstrate that utilizing the fractional Lagrangian approach yields a model that is both valid and flexible, displaying various properties of the physical system under investigation. This approach provides a significant advantage in understanding complex phenomena, which cannot be achieved through classical Lagrangian methods. Indeed, the system characteristics, such as overshoot, settling time, and peak time, vary in the fractional case by changing the value of α. Also, the classical formulation is recovered by the corresponding fractional model when α tends to 1, while their output specifications are completely different. These successful achievements demonstrate diverse properties of physical systems, enhancing the adaptability and effectiveness of the proposed scheme for modelling complex dynamics.
Citation Count: Baleanu, Dumitru...et al. (2012). "Fractional Pais-Uhlenbeck Oscillator", International Journal of Theoretical Physics, Vol. 51. No. 4. pp. 1253-1258.
Fractional Pais-Uhlenbeck Oscillator
(Springer, 2012) Baleanu, Dumitru; Petras, Ivo; Asad, Jihad H.; Pilar Velasco, Maria; 56389; 56389
In this paper we study the fractional Lagrangian of Pais-Uhlenbeck oscillator. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation 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 Count: Defterli, Özlem;...et.al. (2022). "Fractional Treatment: An Accelerated Mass-Spring System", Romanian Reports in Physics, Vol.74, No.4.
Fractional Treatment: An Accelerated Mass-Spring System
(2022) Defterli, Ozlem; Baleanu, Dumitru; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H.; 56389; 31401
The aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and derive the classical equations of motion using the Euler-Lagrange equations of integer-order. Furthermore, the generalized Lagrangian is introduced by using non-integer, so-called fractional, derivative operators; then the resulting fractional Euler-Lagrange equations are generated and solved numerically. The obtained results are presented illustratively by using numerical simulations.
Citation Count: Baleanu, D., Asad, J.H., Petras, I. (2012). Fractional-order two-electric pendulum. Romanian Reports in Physics, 64(4), 907-914.
Fractional-order two-electric pendulum
(Editura Acad Romane, 2012) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo
In this paper we study the fractional Lagrangian of the two-electric pendulum. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation analytically, and numerically. The numerical method used here is based on Grunwald-Letnikov definition of left and right fractional derivatives
Citation Count: Baleanu, Dumitru...et al. (2021). "Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system", Advances in Difference Equations, Vol. 2021, No. 1.
Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system
(2021) Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Asad, Jihad H.; Jajarmi, Amin; Estiri, Elham; 56389
In this paper, the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system are investigated. We mainly analyze, control, and synchronize the associated hyperchaotic behaviors using several approaches. More specifically, the related nonlinear mathematical model is firstly introduced in the forms of both integer- and fractional-order differential equations. Then the related hyperchaotic attractors and phase portraits are analyzed. Next, effectual optimal control approaches are applied to the integer- and fractional-order cases in order to overcome the obnoxious hyperchaotic performance. In addition, two identical hyperchaotic oscillators are synchronized via an adaptive control scheme and an active controller for the integer- and fractional-order mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows a more flexible behavior than its classical counterpart due to its memory effects. Numerical results are also justified theoretically, and computational experiments illustrate the efficacy of the proposed control and synchronization strategies. © 2021, The Author(s).
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, Dumitru; Asad, Jihad H.; Jajarmi, Amin, "New Aspects of the Motion of A Particle In A Circular Cavity", Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, Vol. 9, No. 2, pp. 361-367, (2018)
New Aspects of the Motion of A Particle In A Circular Cavity
(Editura Academiei Romane, 2018) Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; 56389
In this work, we consider the free motion of a particle in a circular cavity. For this model, we obtain the classical and fractional Lagrangian as well as the fractional Hamilton's equations (FHEs) of motion. The fractional equations are formulated in the sense of Caputo and a new fractional derivative with Mittag-Leffler nonsingular kernel. Numerical simulations of the FHEs within these two 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. Simulation results show that the fractional calculus provides more flexible models demonstrating new aspects of the real-world phenomena.
Citation Count: Baleanu, Dumitru...et al. (2019). "New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator", European Physical Journal Plus, Vol. 134, No. 4.
New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator
(Springer Heidelberg, 2019) Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Jajarmi, Amin; Asad, Jihad H.; 56389
Free motion of a fractional capacitor microphone is investigated in this paper. First, a capacitor microphone is introduced and the Euler-Lagrange equations are established. Due to the fractional derivative's the history independence, the fractional order displacement and electrical charge are used in the equations. Fractional differential equations involve in the right- and left-hand-sided derivatives which is reduced to a boundary value problem. Finally, numerical simulations are obtained and dynamical behaviors are numerically discussed.
Citation Count: Akram, Tayyaba...et al. (2020). "Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation", Symmetry-Basel, Vol. 12, No. 7.
Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation
(2020) Akram, Tayyaba; Abbas, Muhammad; Iqbal, Azhar; Baleanu, Dumitru; Asad, Jihad H.; 56389
The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor's series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.
Citation Count: Baleanu, D., Asad, J.H., Petras, I. (2015). Numerical solution of the fractional Euler-Lagrange's equations of a thin elastica model. Nonlinear Dynamics, 81(1-2), 97-102. http://dx.doi.org/10.1007/s11071-015-1975-7
Numerical solution of the fractional Euler-Lagrange's equations of a thin elastica model
(Springer, 2015) Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo
In this manuscript, we investigated the fractional thin elastic system. We studied the obtained fractional Euler-Lagrange's equations of the system numerically. The numerical study is based on Grunwald-Letnikov approach, which is power series expansion of the generating function. We present an illustrative example of the proposed numerical model of the system.
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, Dumitru; Asad, Jihad H.; Alipour, Mohsen (2018), On the motion of a heavy bead sliding on a rotating wire - Fractional treatment, Results in Physics, 11, 579-583.
On the motion of a heavy bead sliding on a rotating wire - Fractional treatment
(Elsevier Science BV, 2018) Baleanu, Dumitru; Asad, Jihad H.; Alipour, Mohsen; 56389
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.
Citation Count: Baleanu, Dumitru...et al. (2020). "Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus", CMES-Computer Modeling in Engineering & Sciences, Vol. 124, No. 3, pp. 953-968.
Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus
(2020) Baleanu, Dumitru; Ghanbari, Behzad; Asad, Jihad H.; Jajarmi, Amin; Pirouz, Hassan Mohammadi; 56389
In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative.
Citation Count: Baleanu, Dumitru...et al. (2021). "The fractional dynamics of a linear triatomic molecule", Romanian Reports in Physics, Vol. 73, No. 1.
The fractional dynamics of a linear triatomic molecule
(2021) Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Jajarmi, Amin; Defterli, Özlem; Asad, Jihad H.; 56389
In this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.
Citation Count: Baleanu, Dumitru...et al. (2020). "The fractional features of a harmonic oscillator with position-dependent mass", Communications in Theoretical Physics, Vol. 72, No. 5.
The fractional features of a harmonic oscillator with position-dependent mass
(2020) Baleanu, Dumitru; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Asad, Jihad H.; 56389
In this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as an introduction, we give a full description of the system by constructing its classical Lagrangian; thereupon, we derive the related classical equations of motion such as the classical Euler-Lagrange equations. Secondly, we fractionalize the classical Lagrangian of the system, and then we obtain the corresponding fractional Euler-Lagrange equations (FELEs). As a final step, we give the numerical simulations corresponding to the FELEs within different fractional operators. Numerical results based on the Caputo and the Atangana-Baleanu-Caputo (ABC) fractional derivatives are given to verify the theoretical analysis.
Citation Count: Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin, "The Fractional Model of Spring Pendulum: New Features Within Different Kernels", Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, Vol. 19, No. 3, pp. 447-454, (2018)
The Fractional Model of Spring Pendulum: New Features Within Different Kernels
(Editura Academiei Romane, 2018) Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; 56389
In this work, new aspects of the fractional calculus (FC) are examined for a model of spring pendulum in fractional sense. First, we obtain the classical Lagrangian of the model, and as a result, we derive the classical Euler-Lagrange equations of the motion. Second, we generalize the classical Lagrangian to fractional case and derive the fractional Euler-Lagrange equations in terms of fractional derivatives with singular and nonsingular kernels, respectively. Finally, we provide the numerical solution of these equations within two fractional operators for some fractional orders and initial conditions. Numerical simulations verify that taking into account the recently features of the FC provides more realistic models demonstrating hidden aspects of the real-world phenomena.