Abstract：
:The objective of this paper is to study the optimal control problem for the fractional tuberculosis (TB) infection model including the impact of diabetes and resistant strains. The governed model consists of 14 fractional-order (FO) equations. Four control variables are presented to minimize the cost of interventions. The fractional derivative is defined in the Atangana-Baleanu-Caputo (ABC) sense. New numerical schemes for simulating a FO optimal system with Mittag-Leffler kernels are presented. These schemes are based on the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. We introduce a simple modification of the step size in the two-step Lagrange polynomial interpolation to obtain stability in a larger region. Moreover, necessary and sufficient conditions for the control problem are considered. Some numerical simulations are given to validate the theoretical results.
journal_name
J Adv Resjournal_title
Journal of advanced researchauthors
Sweilam NH,Al-Mekhlafi SM,Baleanu Ddoi
10.1016/j.jare.2019.01.007subject
Has Abstractpub_date
2019-01-19 00:00:00pages
125-137eissn
2090-1232issn
2090-1224pii
S2090-1232(19)30006-2journal_volume
17pub_type
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