Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 4Citation - Scopus: 3On 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 FThis 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: 7Citation - Scopus: 8On the New Hadamard Fractional Optimal Control Problems(Sage Publications Ltd, 2023) Tajani, Asmae; Jajarmi, Amin; Baleanu, Dumitru; Zguaid, KhalidThe 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: 27Citation - Scopus: 28Fractional Investigation of Time-Dependent Mass Pendulum(Sage Publications Ltd, 2024) Defterli, Ozlem; Wannan, Rania; Sajjadi, Samaneh S.; Asad, Jihad H.; Baleanu, Dumitru; Jajarmi, AminIn 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 & alpha;. Also, the classical formulation is recovered by the corresponding fractional model when & alpha; 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.Article Citation - WoS: 21Citation - Scopus: 26Robust Stabilization of Fractional-Order Chaotic Systems With Linear Controllers: Lmi-Based Sufficient Conditions(Sage Publications Ltd, 2014) Kuntanapreeda, Suwat; Delavari, Hadi; Baleanu, Dumitru; Faieghi, Mohammad RezaThis paper is concerned with the problem of robust state feedback controller design to suppress fractional-order chaotic systems. A general class of fractional-order chaotic systems is considered and it is assumed that the systems' equations depend on bounded uncertain parameters. We transform the chaotic system equations into linear interval systems, and a sufficient stabilizability condition is derived in terms of linear matrix inequality (LMI). Then, an appropriate feedback gain is introduced to bring the chaotic states to the origin. Such design will result in a simple but effective controller. Several numerical simulations have been carried out to verify the effectiveness of the theoretic results.Article Citation - WoS: 9Citation - Scopus: 11Research on a Collocation Approach and Three Metaheuristic Techniques Based on Mvo, Mfo, and Woa for Optimal Control of Fractional Differential Equation(Sage Publications Ltd, 2023) Khanduzi, Raheleh; Beik, Samaneh P. A.; Baleanu, Dumitru; Ebrahimzadeh, Asiyeh; A Beik, Samaneh PExploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann-Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.Article Citation - WoS: 7Citation - Scopus: 8Dynamical Analysis and Triple Compound Combination Anti-Synchronization of Novel Fractional Chaotic System(Sage Publications Ltd, 2022) Jahanzaib, Lone S.; Nasreen; Baleanu, Dumitru; Trikha, Pushali; Nasreen, Lone SThis study introduces a novel 3-D fractional chaotic system with two quadratic terms and no equilibrium point. Thorough dynamical analysis of the introduced system is done studying Lyapunov dynamics with respect to fractional order and parameter value, Kaplan-Yorke dimension, bifurcation analysis, phase portraits, existence, and uniqueness of solution, dissipative and symmetric character, etc. The novel system is anti-synchronized using the novel technique 'triple compound combination' considering uncertainties and disturbances on a parallel system by two methods-nonlinear and adaptive sliding mode control. A proposed application of achieved synchronization in secure communication is presented. A comparative study of obtained results with published literature is also presented.Article Citation - WoS: 42Citation - Scopus: 44A Numerical Approach for Solving Fractional Optimal Control Problems With Mittag-Leffler Kernel(Sage Publications Ltd, 2022) Ganji, Roghayeh M.; Sayevand, Khosro; Baleanu, Dumitru; Jafari, HosseinIn this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana-Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.Article Citation - WoS: 8Citation - Scopus: 7A New Generalization of the Fractional Euler-Lagrange Equation for a Vertical Mass-Spring(Sage Publications Ltd, 2021) Ullah, Malik Zaka; Mallawi, Fouad; Alshomrani, Ali Saleh; Baleanu, Dumitru; Saleh Alshomrani, AliIn this new study, we investigate the motion of a forced mass-spring-damper in a vertical position. First, the classical Lagrangian as well as the classical Euler-Lagrange equation of motion are constructed. Then the fractional Euler-Lagrange equation is derived by extending the classical Lagrangian in the fractional sense. In this extension, a new form of the fractional derivative is employed including a general function as its kernel. The derived fractional Euler-Lagrange equation is then converted into a system of linear algebraic equation by designing an efficient matrix approximation approach. The numerical findings are reported verifying the theoretical investigations. According to the results, some remarkable thinks are achieved; indeed, the numerical simulations show that different aspects of the system under study can be explored with regard to the flexibility found in selecting the kernel contrary to the traditional fractional models.Article Citation - WoS: 86Citation - Scopus: 93Solving Multi-Dimensional Fractional Optimal Control Problems With Inequality Constraint by Bernstein Polynomials Operational Matrices(Sage Publications Ltd, 2013) Rostamy, Davood; Baleanu, Dumitru; Alipour, MohsenIn this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.Editorial Citation - WoS: 24Citation - Scopus: 24New Trends in Fractional Dynamics(Sage Publications Ltd, 2014) Baleanu, Dumitru; Chen, Wen; Sabatier, Jocelyn; Tenreiro Machado, Jose A.; Machado, José A Tenreiro