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OPTIMAL CONTROL WITH FINAL OBSERVATION OF A FRACTIONAL DIFFUSION WAVE EQUATION

Abstract : We consider a controlled fractional diffusion wave equation involving Riemann-Liouville fractional derivative or order α ∈ (1, 2). First we prove by means of eigenfunction expansions the existence of solutions to such equations. Then we show that we can approach the fractional integral of order 2 − α of the state at final time by a desired state by acting on the control. Using the first order Euler-Lagrange optimality, we obtain the characterization of the optimal control.
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https://hal.archives-ouvertes.fr/hal-02548503
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Submitted on : Monday, April 20, 2020 - 5:09:18 PM
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Gisèle Mophou, C. Joseph. OPTIMAL CONTROL WITH FINAL OBSERVATION OF A FRACTIONAL DIFFUSION WAVE EQUATION. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, Watam Press, 2016. ⟨hal-02548503⟩

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