Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Yakar, Coşkun (2010)
Abstract and Applied Analysis
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Displaying similar documents to “Exact solution of impulse response to a class of fractional oscillators and its stability.”
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Stability analysis of fractional differential systems with order lying in .
Zhang, Fengrong, Li, Changpin (2011)
Advances in Difference Equations [electronic only]
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Fractional order calculus: basic concepts and engineering applications.
Gutiérrez, Ricardo Enrique, Rosário, João Maurício, Machado, José Tenreiro (2010)
Mathematical Problems in Engineering
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From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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Design of unknown input fractional-order observers for fractional-order systems
Ibrahima N'Doye, Mohamed Darouach, Holger Voos, Michel Zasadzinski (2013)
International Journal of Applied Mathematics and Computer Science
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This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach,...
Synchronization of fractional-order chaotic systems with multiple delays by a new approach
Jianbing Hu, Hua Wei, Lingdong Zhao (2015)
Kybernetika
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In this paper, we propose a new approach of designing a controller and an update rule of unknown parameters for synchronizing fractional-order system with multiple delays and prove the correctness of the approach according to the fractional Lyapunov stable theorem. Based on the proposed approach, synchronizing fractional delayed chaotic system with and without unknown parameters is realized. Numerical simulations are carried out to confirm the effectiveness of the approach.
Recent applications of fractional calculus to science and engineering.
Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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Modelling of Piezothermoelastic Beam with Fractional Order Derivative
Rajneesh Kumar, Poonam Sharma (2016)
Curved and Layered Structures
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This paper deals with the study of transverse vibrations in piezothermoelastic beam resonators with fractional order derivative. The fractional order theory of thermoelasticity developed by Sherief et al. [1] has been used to study the problem. The expressions for frequency shift and damping factor are derived for a thermo micro-electromechanical (MEM) and thermo nano-electromechanical (NEM) beam resonators clamped on one side and free on another. The effect of fractional order derivative...
Synchronization of chaotic fractional-order WINDMI systems via linear state error feedback control.
Xin, Baogui, Chen, Tong, Liu, Yanqin (2010)
Mathematical Problems in Engineering
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Chaos synchronization between two different fractional systems of Lorenz family.
Matouk, A.E. (2009)
Mathematical Problems in Engineering
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On Riemann-Liouville and Caputo derivatives.
Li, Changpin, Qian, Deliang, Chen, Yangquan (2011)
Discrete Dynamics in Nature and Society
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A Fractional LC − RC Circuit
Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05 We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution...