Boundary Control of Fractional Partial Differential Equations

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Boundary Control of Fractional Partial Differential Equations

Alqarni, Faez Ali

01/2016

Dissertation

We propose to stabilize time and/or space fractional heat-wave-like equations using boundary control. We derive and investigate the controllers based on the backstepping method (transmutation) and show that these controllers stabilized the unstable fractional partial di¤erential equations. Stability of the overall system-controller is demonstrated. We use the Caputo fractional derivative. It is well-know that the fractional di¤usion and wave equations are derived from the classical di¤usion and wave equations by changing the integer order derivative by appropriate orders of fractional derivatives. Numerical simulations are given to illustrate the e¤ectiveness of the approaches.

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