Fractional order calculus: basic concepts and engineering applications
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Publication:980589
DOI10.1155/2010/375858zbMath1190.26002OpenAlexW2069295222WikidataQ58653043 ScholiaQ58653043MaRDI QIDQ980589
João Maurício Rosário, Ricardo Enrique Gutiérrez, José António Tenreiro Machado
Publication date: 29 June 2010
Published in: Mathematical Problems in Engineering (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/228743
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Cites Work
- Unnamed Item
- Unnamed Item
- A generalised fractional derivative approach to viscoelastic material properties measurement
- Fractional-order system identification based on continuous order-distributions
- A method for modelling and simulation of fractional systems
- Fractional generalized splines and signal processing
- Approximation and identification of diffusive interfaces by fractional models
- The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
- Recent applications of fractional calculus to science and engineering
- Anlogue realizations of fractional-order controllers.
- Fractional motion control: Application to an XY cutting table
- Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators
- Fractional-order dynamical models of love
- On the Appearance of the Fractional Derivative in the Behavior of Real Materials
- Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function
- Nonconservative Systems within Fractional Generalized Derivatives
- Identification of Complex Order-distributions
- Fractional Multi-models of the Frog Gastrocnemius Muscle
- Modeling the Cardiac Tissue Electrode Interface Using Fractional Calculus
- Automatic Loop Shaping in QFT Using CRONE Structures
- Dynamic Measurements in Long-memory Materials: Fractional Calculus Evaluation of Approach to Steady State
- Design of Optimum Systems of Viscoelastic Vibration Absorbers for a Given Material Based on the Fractional Calculus Model
- From fractal robustness to the CRONE approach
- Fractional Order PDαJoint Control of Legged Robots
- Optimal Fractional Controllers for Rational Order Systems: A Special Case of the Wiener-Hopf Spectral Factorization Method
- Physical and geometrical interpretation of fractional operators
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