Fractional control of heat diffusion systems

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Stability of Fractional-Order Systems with Rational Orders (2008, unknown): “The fractional order calculus plays an important role in physics [45,60,67], thermodynamics [31,57], electrical circuits theory and fractances [7,12,14,21,40,71], mechatronics systems [55], signal processing [56, 68], chemical mixing [41], chaos theory [62, 64], and biological system as well [23].”
Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation (2014, background): “Recently, several numerical techniques are investigated for achieving high accurate solutions for classical fractional differential equations (see for instance [10–18]).”
Fractional variational optimal control problems with delayed arguments (2010, methodology): “In control theory the fractional calculus was used by several authors, and interesting results were reported [15–19].”
Rational approximation for fractional-order system by particle swarm optimization (2012, background): “cn in engineering [1], for example, in heat diffusion modeling and control [2–4], the fractional-order PID controller [5–7], fractional-order chaotic systems [8–10], the fractional-order digital filter [11, 12], etc.”
Stability analysis of Caputo fractional-order nonlinear systems revisited (2011, background): “In recent years, numerous studies and applications of fractionalorder systems in many areas of science and engineering have been presented [1–11].”