Fractional Order Systems: Modeling and Control Applications

By R. Caponetto, G. Dongola, L. Fortuna, Ivo Petrás. 2010

878 citations recorded by the source corpus.

Fractional Order Systems Fractional Order PID Controller Chaotic Fractional Order Systems Field Programmable Gate Array, Microcontroller and Field Programmable Analog Array Implementation Switched Capacitor and Integrated Circuit Design Modeling of Ionic Polymeric Metal Composite

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/3b8913a171acd0cd9ef828bec47e1cc7547db50d

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In Control and Systems Engineering

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Citations in the corpus

Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives (2013, background): “Introduction In the recent years considerable interest in the theory and applications of fractional differential equations has been demonstrated, see for example ([1, 3, 15, 8, 17, 19]).”
The Chronicles of Fractional Calculus (2017, neutral): “2009 [6, 90, 122, 27, 89, 77, 155] [109, 17] 2010 [111, 31, 133, 165, 46] [98, 106, 63] 2011 [156, 144, 87, 65, 126, 92, 3, 187, 207, 78, 44, 93] [86, 18]”
The Role of the Mittag-Leffler Function in Fractional Modeling (2015, background): “We also mention here a growing number of applications of the Mittag-Leffler function in control theory (see [11,13,16].”
Tuning and implementation methods for fractional-order controllers (2012, methodology): “An analogue implementation was proposed in the book [26] and a digital implementation was suggested in the book [6].”
Fractional-order delayed predator–prey systems with Holling type-II functional response (2015, background): “Examples of fractional-order systems in modeling and control may be found in [5,27,28].”
A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors (2018, background): “If α1, · · · , αn are all positive integer multiples of a real number γ, then (6) is a commensurate fractional-order system of order γ; otherwise, it is said to be incommensurate, with more degrees of freedom to fit system dynamics [19, 31, 32].”
Fractional calculus: A survey of useful formulas (2013, background): “– To find more information on the topic consider in the section consult, for instance, [14–18] and the references included in it.”
An $L_q(L_p)$-theory for the time fractional evolution equations with variable coefficients (2015, background): “Introduction Fractional calculus has been used in numerous areas including mathematical modeling [24, 44], control engineering [6, 32], electromagnetism [13, 43], polymer science [3, 29], hydrology [4, 41], biophysics [14, 22], and even finance [36, 40].”
Science metrics on fractional calculus development since 1966 (2013, background): “Figure 2 (left) depicts the evolution of Da [19, 12, 56, 75, 57, 99, 60, 87, 100, 100, 77, 68, 85, 95, 69, 70, 71, 72, 78, 23, 102, 13, 96, 64, 114, 36, 79, 73, 91, 63, 84, 80, 105, 109, 4, 111, 82, 22, 27, 28, 110, 81, 67, 32, 29, 86, 52, 33, 117, 106, 55, 58, 112, 113, 108, 6, 15, 2, 41, 59, 10, 4”
Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces (2013, neutral): “[14] (control theory), Metzler et al.”