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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Displaying similar documents to “Normalized finite fractional differences: Computational and accuracy breakthroughs”
Fractional order calculus: basic concepts and engineering applications.
Time-delay and fractional derivatives.
Machado, J.A.Tenreiro (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,...
Exact solution of impulse response to a class of fractional oscillators and its stability.
Li, Ming, Lim, S.C., Chen, Shengyong (2011)
Mathematical Problems in Engineering
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Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers.
Delshad, Saleh Sayyad, Asheghan, Mohammad Mostafa, Beheshti, Mohammadtaghi Hamidi (2010)
Advances in Difference Equations [electronic only]
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Recent applications of fractional calculus to science and engineering.
Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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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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An effective numerical method and its utilization to solution of fractional models used in bioengineering applications.
Petráš, Ivo (2011)
Advances in Difference Equations [electronic only]
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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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From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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Positivity and stability of fractional descriptor time-varying discrete-time linear systems
Tadeusz Kaczorek (2016)
International Journal of Applied Mathematics and Computer Science
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The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor timevarying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders
Łukasz Sajewski (2017)
International Journal of Applied Mathematics and Computer Science
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Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is...
Discrete fractional calculus with the nabla operator.
Atici, F.M., Eloe, P. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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