Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Jajarmi, AminSubject: search.filters.subject.Fractional Calculus

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Now showing 1 - 10 of 11
  • Article
    Citation - WoS: 59
    Citation - Scopus: 66
    New Aspects of the Motion of a Particle in a Circular Cavity
    (Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; Matematik
    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.
  • Article
    Citation - WoS: 81
    Citation - Scopus: 94
    The Fractional Dynamics of a Linear Triatomic Molecule
    (Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; Matematik
    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.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 3
    On Generalized Asymmetric Harmonic Oscillator With Quadratic Nonlinearity Within Fractional Variational Principles
    (Sage Publications Ltd, 2024) Baleanu, Dumitru; Jajarmi, Amin; Defterli, Ozlem; Mohammad, Noorhan F. AlShaikh; Asad, Jihad; AlShaikh Mohammad, Noorhan F
    This work studies the nonlinear fractional dynamics of asymmetric harmonic oscillators. The classical description of the physical system is generalized using the principles of fractional variational analysis. As a system of two-coupled fractional differential equations with a quadratic nonlinear component, the fractional Euler-Lagrange equations of the motion of the corresponding system are obtained. The Adams-Bashforth predictor-corrector numerical approach is used to approximate the system's outcomes, which are then simulated comparatively with respect to various model parameter values, including mass, linear and quadratic nonlinear stiffness, and the order of the fractional derivative. The simulations provided the possibility of investigating various dynamical behaviours within the same physical model that is generalized by the use of fractional operators.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    On the New Hadamard Fractional Optimal Control Problems
    (Sage Publications Ltd, 2023) Tajani, Asmae; Jajarmi, Amin; Baleanu, Dumitru; Zguaid, Khalid
    The main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered problem are derived in terms of the corresponding Euler-Lagrange equations. An iterative method is also proposed to numerically solve the obtained equations from the necessary optimality conditions. Two illustrative examples are considered and simulated in order to show the applicability and efficiency of the proposed method. Numerical simulations show that the used method presents some satisfying results regarding the absolute error values.
  • Article
    Citation - WoS: 101
    Citation - Scopus: 115
    On a Nonlinear Dynamical System With Both Chaotic and Nonchaotic Behaviors: a New Fractional Analysis and Control
    (Springer, 2021) Jajarmi, Amin; Defterli, Ozlem; Baleanu, Dumitru; Sajjadi, Samaneh Sadat
    In this paper, we aim to analyze the complicated dynamical motion of a quarter-car suspension system with a sinusoidal road excitation force. First, we consider a new mathematical model in the form of fractional-order differential equations. In the proposed model, we apply the Caputo-Fabrizio fractional operator with exponential kernel. Then to solve the related equations, we suggest a quadratic numerical method and prove its stability and convergence. A deep investigation in the framework of time-domain response and phase-portrait shows that both the chaotic and nonchaotic behaviors of the considered system can be identified by the fractional-order mathematical model. Finally, we present a state-feedback controller and a chaos optimal control to overcome the system chaotic oscillations. Simulation results demonstrate the effectiveness of the proposed modeling and control strategies.
  • Article
    Citation - WoS: 117
    Citation - Scopus: 135
    Hyperchaotic Behaviors, Optimal Control, and Synchronization of a Nonautonomous Cardiac Conduction System
    (Springer, 2021) Sajjadi, Samaneh Sadat; Asad, Jihad H.; Jajarmi, Amin; Estiri, Elham; Baleanu, Dumitru
    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.
  • Article
    Citation - WoS: 88
    Citation - Scopus: 94
    New Aspects of Time Fractional Optimal Control Problems Within Operators With Nonsingular Kernel
    (Amer inst Mathematical Sciences-aims, 2020) Jajarmi, Amin; Yildiz, Burak; Baleanu, Dumitru; Yildiz, Tugba Akman
    This paper deals with a new formulation of time fractional optimal control problems governed by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is derived, which contains the forward and backward fractional differential equations in the sense of CF. These equations are then expressed in terms of Volterra integrals and also solved by a new numerical scheme based on approximating the Volterra integrals. The linear rate of convergence for this method is also justified theoretically. We present three illustrative examples to show the performance of this method. These examples also test the contribution of using CF derivative for dynamical constraints and we observe the efficiency of this new approach compared to the classical version of fractional operators.
  • Article
    Citation - WoS: 127
    Citation - Scopus: 154
    A New Iterative Method for the Numerical Solution of High-Order Non-Linear Fractional Boundary Value Problems
    (Frontiers Media Sa, 2020) Baleanu, Dumitru; Jajarmi, Amin
    The boundary value problems (BVPs) have attracted the attention of many scientists from both practical and theoretical points of view, for these problems have remarkable applications in different branches of pure and applied sciences. Due to this important property, this research aims to develop an efficient numerical method for solving a class of non-linear fractional BVPs. The proposed method is free from perturbation, discretization, linearization, or restrictive assumptions, and provides the exact solution in the form of a uniformly convergent series. Moreover, the exact solution is determined by solving only a sequence of linear BVPs of fractional-order. Hence, from practical viewpoint, the suggested technique is efficient and easy to implement. To achieve an approximate solution with enough accuracy, we provide an iterative algorithm that is also computationally efficient. Finally, four illustrative examples are given verifying the superiority of the new technique compared to the other existing results.
  • Article
    Citation - WoS: 85
    Citation - Scopus: 97
    Suboptimal Control of Fractional-Order Dynamic Systems With Delay Argument
    (Sage Publications Ltd, 2018) Baleanu, Dumitru; Jajarmi, Amin
    In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler-Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grunwald-Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement.
  • Article
    Citation - WoS: 80
    Citation - Scopus: 93
    A New Formulation of the Fractional Optimal Control Problems Involving Mittag-Leffler Nonsingular Kernel
    (Springer/plenum Publishers, 2017) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, Dumitru
    The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag-Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Gronwall's inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.