OPTIMAL CONTROL OF DIFFUSION EQUATION WITH FRACTIONAL TIME DERIVATIVE WITH NONLOCAL AND NONSINGULAR MITTAG-LEFFLER KERNEL

Abstract : In this paper, we consider a diffusion equation with fractional-time derivative with non-singular Mittag-Leffler kernel in Hilbert spaces. Existence and uniqueness of solution are proved by means of a spectral argument. The existence of solution is obtained for all values of the fractional parameter α ∈ (0, 1). Moreover, by applying control theory to the fractional diffusion problem we obtain an optimality system which has also a unique solution.
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Submitted on : Wednesday, December 18, 2019 - 6:49:44 PM
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J Djida, Gisèle Mophou, I Area. OPTIMAL CONTROL OF DIFFUSION EQUATION WITH FRACTIONAL TIME DERIVATIVE WITH NONLOCAL AND NONSINGULAR MITTAG-LEFFLER KERNEL. Journal of Optimization Theory and Applications, Springer Verlag, 2018, 182 (2), pp.540-557. ⟨10.1007/s10957-018-1305-6⟩. ⟨hal-02418470⟩

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