Mehandiratta V, Mehra M, Leugering G (2022)
Publication Type: Journal article
Publication year: 2022
Book Volume: 51
Pages Range: 191-226
Journal Issue: 2
We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial fractional derivatives of Sturm-Liouville type. We first prove existence and uniqueness of solutions of STFPEs on an open bounded interval and study their regularity. Then we show existence and uniqueness of solutions to a quadratic distributed optimal control problem. We derive an adjoint problem using the right-Caputo derivative in time and provide optimality conditions for the control problem. Moreover, we propose a finite difference scheme to find the approximate solution of the considered optimal control problem. In the proposed scheme, the well-known L1 method has been used to approximate the time-fractional Caputo derivative, while the spatial derivative is approximated using the Grünwald-Letnikov formula. Finally, we demonstrate the accuracy and the performance of the proposed difference scheme via examples.
APA:
Mehandiratta, V., Mehra, M., & Leugering, G. (2022). Distributed optimal control problems driven by space-time fractional parabolic equations. Control and Cybernetics, 51(2), 191-226. https://doi.org/10.2478/candc-2022-0014
MLA:
Mehandiratta, Vaibhav, Mani Mehra, and Günter Leugering. "Distributed optimal control problems driven by space-time fractional parabolic equations." Control and Cybernetics 51.2 (2022): 191-226.
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