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.

Mechanical degradation hampers the practical usage of polymers for turbulent drag reduction
application. Mechanical degradation refers to the chemical process in which the activation energy of
polymer chain scission is exceeded by mechanical action on the polymer chain, and bond rupture
occurs. When a water-soluble polymer and surfactant are mixed in water solution, the specific structures
(aggregates) are formed, in which polymer film is formed around micelle. In this work, Xanthan gum (XG) –
Sodium lauryl ether sulfate (SELS) complex formation and its effect on percentage viscosity reduction
(%VR) was studied. It was found that SELS surfactant reduced the mechanical degradation of XG much
more efficiently than th

Efficacy of Varnishes with: Bioactive Glass, Recaldent Technology and Silver Diamine Fluoride in Comparison with Sodium Fluoride on Tooth Surface Micro-hardness (an In Vitro Study)

Abstract: Microfluidic devices present unique advantages for the development of efficient drug assay and screening. The microfluidic platforms might offer a more rapid and cost-effective alternative. Fluids are confined in devices that have a significant dimension on the micrometer scale. Due to this extreme confinement, the volumes used for drug assays are tiny (milliliters to femtoliters).

 In this research, a microfluidic chip consists of micro-channels carved on substrate materials built by using Acrylic (Polymethyl Methacrylate, PMMA) chip was designed using a Carbon Dioxide (CO₂) laser machine. The CO2 parameters have influence on the width, depth, roughness of the chip. In order to have regular

A mathematical model constructed to study the combined effects of the concentration and the thermodiffusion on the nanoparticles of a Jeffrey fluid with a magnetic field effect the process of containing waves in a three-dimensional rectangular porous medium canal. Using the HPM to solve the nonlinear and coupled partial differential equations. Numerical results were obtained for temperature distribution, nanoparticles concentration, velocity, pressure rise, pressure gradient, friction force and stream function. Through the graphs, it was found that the velocity of fluid rises with the increase of a mean rate of volume flow and a magnetic parameter, while the velocity goes down with the increasing a Darcy number and lateral walls. Also, t

The study was conducted to assess the attitude and awareness of a sample of people regarding the indiscriminate slaughter and its effects on health and the environment compared with slaughtering  in a slaughterhouse. The sample consisted of 120 persons from six equal professional groups contacted with the butchery labour (livestock keeper, truck driver, butcher, veterinarian, shopkeeper and consumer). The age ranged 22-76 years old, mean 52±10  years, lived ≥ 5 years in the Baghdad city. The results showed that there is a preference for slaughtering inside the slaughterhouse due to the presence of veterinary examination, slaughtering and preparing meat in a healthy, easy-to-clean places, unlike the indiscriminate sla