Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel

Jean-Daniel Djida (), Gisèle Mophou () and Iván Area ()
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Jean-Daniel Djida: Universidade de Santiago de Compostela
Gisèle Mophou: African Institute for Mathematical Sciences (AIMS)
Iván Area: Universidade de Vigo

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 2, No 5, 540-557

Abstract: Abstract In this paper, we consider a diffusion equation with fractional time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. We first prove the existence and uniqueness of solution by means of a spectral argument. Then, we consider a distributed controlled fractional diffusion problem. We show that there exists a unique optimal control, which can act on the system in order to approach the state of the system by a given state at minimal cost. Finally, using the Euler–Lagrange first-order optimality condition, we obtain an optimality system, which characterizes the optimal control.

Keywords: Mittag-Leffler functions; Time-fractional differential equation; Optimality system; Euler–Lagrange optimality conditions; 49J20; 49K20; 26A33 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-018-1305-6

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