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.

The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil

Purpose: This study aimed to evaluate the influence of vitamin D3 levels on bone density, primary dental implant stability, and successful osseointegration.

Materials and Methods: Clinical and radiological examination with a standardized cone‐beam computed tomography (CBCT) machine and laboratory investigation for serum levels of vitamin D3 were performed for all patients. Only patients in need of single or multiple straightforward dental implant surgery in either jaw with no history of systemic disease or condition that may interfere with bone healing were included in this study to receive the dental implant by the same oral and maxillofacial surgeon, which re‐opened

A cumulative review with a systematic approach aimed to provide a comparison of studies’ investigating the possible impact of the active form of vitamin D3, calcitriol (CTL), on the tooth movement caused by orthodontic forces (OTM) by evaluating the quality of evidence, based on collating current data from animal model studies, in vivo cell culture studies, and human clinical trials. Methods: A strict systematic review protocol was applied following the application of the International Prospective Register of Systematic Reviews (PROSPERO). A structured search strategy, including main keywords, was defined during detailed search with the application of electronic database systems: Medline/Pubmed, EMBASE, Scopus, Web of Science, and

The new novel polymers nanocomposites based modified chitosan (CS) blending with polyvinyl alcohol (PVA) and coated gold or silver nanoparticles (AuNPs), AgNPs) were synthesized from many sequence reactions as presented in (Scheme1, 2 and 3). By utilizing 1H-NMR spectroscopy, FTIR, and Field Emission Scanning electron microscope , the synthesized compounds have been identified. Molecular docking is studied, where operations are used to predict the binding status of compounds with the enzyme and to calculate the free energy (ΔG) of the compounds prepared. Also, the antibacterial activity regarding the synthesized compounds against two resistant pathogenic bacteria (G+) S. aureus and E. coli (G-) was examined in vitro compare with standard a

Objectives. This study aimed at finding out whether anterior teeth angulation and inclination have a relationship with the maxillary teeth and dental arch dimensions. Methods. Fifty study models with normal occlusion were selected from the archive of the Department of Orthodontics at Baghdad Dental Faculty. Maxillary dental arch width and length at different points were determined in addition to measuring anterior teeth angulation, inclination, crown thickness, overjet, overbite, and Bolton’s ratios. The unpaired t-test and Pearson’s correlation coefficient test were used for data analysis. Results. No statistical gender differences were reported in all measurements except the dental arch widths and length where males had signif