Optimal control problem for coupled time-fractional diffusion systems with final observations. Issue 1 (11th December 2019)

• Record Type: Journal Article
• Authors: Bahaa, G. M.; Hamiaz, A.
• Is Part Of: Journal of Taibah University for science. Volume 13:Issue 1(2019)
• Page Start: 124
• Page End: 135
• Publication Date: 2019-12-11
• Subjects: Optimal control -- coupled time-fractional system -- Atangana–Baleanu derivative -- diffusion equations -- wave equations; 46C05 -- 49J20 -- 93C20; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2018.1545560
• Languages: English
• ISSNs: 1658-3655

Abstract

ABSTRACT: In this paper, fractional optimal control problem for two-dimensional coupled diffusion system with final observation is investigated. The fractional time derivative is considered in Atangana–Baleanu sense. Constraints on controls are imposed. First, by means of the classical control theory, the existence and uniqueness of the state for these systems is proved. Then, the necessary and sufficient optimality conditions for the fractional Dirichlet problems with the quadratic performance functional are derived. Finally we give some examples to illustrate the applicability of our results. The optimization problem presented in this paper constitutes a generalization of the optimal control problem of diffusion equations with Dirichlet boundary conditions considered in recent papers to coupled systems with Atangana–Baleanu time derivatives.