In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
An experimental and numerical study was carried out to investigate the heat transfer by natural convection in a three dimensional annulus enclosure filled with porous media (silica sand) between two inclined concentric cylinders with (and without) annular fins attached to the inner cylinder under steady state condition. The experiments were carried out for a range of modified Rayleigh number (0.2 ≤Ra*≤ 11) and extended to Ra*=500 for numerical study and for annulus inclination angle of (δ = 0˚, 30˚, 60˚ and 90˚). The numerical study was to give the governing equation under assumptions that used Darcy law and Boussinesq’s approximation and then it was solved numerically using finite difference approximation. It was found that t
... Show MoreABSTRACT Background: Polycystic ovarian syndrome (PCOS) is one of the most important reproductive and endocrine disorders in women at reproductive age. It's associated with metabolic disorder, obesity, insulin resistance and oxidative stress chronic periodontitis and PCOS both of them associated with low chronic grade of inflammation. The prevalence of periodontal disease seems to be higher in women with PCOS. Superoxide dismutase enzyme (SOD) is an important circulating marker and protecting enzyme helping the body tissues to get rid of reactive oxygen species (ROS) that damage the tissue. Aim of the study: The aim of this study was to measure and compare the levels of (SOD) among group of chronic periodontitis patients with PCOS, group
... Show MoreThree hundred and fifty five patients with hepatitis were investigated in this study all cases gave negative result with HBs Ag , IgM-anti HCV , IgM-anti HEV, IgM-anti HDV and anti-HIV tests . The frequency of IgM-anti HAV was 113 and the percentage was 32 % in all ages but when these patients divided into five groups dependent on ages. The highest percentage of IgM-anti HAV was (45%) in age <10 and the percentage declined with age increase till to 9% in age >41 year.
The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
... Show MoreRheumatoid arthritis (RA) is characterized by persistent joint inflammation, which is a defining feature of this chronic inflammatory condition. Considerable advancements have been made in the field of disease-modifying anti-rheumatic medicines (DMARDs), which effectively mitigate inflammation and forestall further joint deterioration. Anti-tumor necrosis factor-alpha (TNF-α) drugs, which are a class of biological DMARDs (bDMARDs), have been efficaciously employed in the treatment of RA in recent times Adalimumab, a TNF inhibitor, has demonstrated significant efficacy in reducing disease symptoms and halting disease progression in patients with RA. However, its use is associated with major side effects and high costs. In addition,
... Show MoreIntroduction and Aim: Graves ophthalmopathy is one of the pandemic public health disorders in Iraq. The current investigation attempts to determine the variation in the complete total blood cells on the recovery of individuals with Graves' ophthalmopathy following low and high-dose Radioactive Iodine 131 (RI-131) exposures. Materials and Methods: The complete blood CBC level in people with Graves' illness and healthy, normal controls were quantitatively identified using the CBC counter. Thyroid stimulating hormone was utilized to compare the recovery of ophthalmopathy patients in comparison to a control group. Results: In comparison to healthy controls, patients with Graves' ophthalmopathy disease who received 10 mci of RAI-
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