Fractional calculus has paid much attention in recent years, because it plays an essential role in many fields of science and  engineering, where the study of stability theory of fractional differential equations emerges to be very important. In this paper, the stability of fractional order ordinary differential equations will be studied and introduced the backstepping method. The Lyapunov function  is easily found by this method. This method also gives a guarantee of stable solutions for the fractional order differential equations. Furthermore it gives asymptotically stable.

ABSTRACT Background: One of the challenges to use chlorhexidine is its effect on the amount of microleakage after restoration; however, use of the materials with antibacterial properties after tooth preparation and before restoration has been widespread. The objective of this, in-vitro, study was to evaluate the influence of consepsis (chlorhexidine gloconate disinfectant) application on microleakage in class II cavities restored with light cured composite using universal adhesive system; etch and rinse technique –self etch technique. Materials and Methods: Forty class II cavities were prepared on mesial and distal surfaces of 20 non-carious mandibular third molars. The cavities were divided into four groups; (n =10 for each group).

Chilled ceilings systems offer potential for overall capital savings. The main aim of the present research is to investigate the thermal performance of the indirect contact closed circuit cooling tower, ICCCCT used with chilled ceiling, to gain a deeper knowledge in this important field of engineering which has been traditionally used in various industrial & HVAC systems. To achieve this study, experimental work were implemented for the ICCCCT use with chilled ceiling. In this study the thermal performances of closed wet cooling tower use with chilled ceiling is experimentally and theoretically investigated. Different experimental tests were conducted by varying the controlling parameters to investigate their effects

Autonomous systems are these systems which power themselves from the available ambient energies in addition to their duties. In the next few years, autonomous systems will pervade society and they will find their ways into different applications related to health, security, comfort and entertainment. Piezoelectric harvesters are possible energy converters which can be used to convert the available ambient vibration energy into electrical energy. In this contribution, an energy harvesting cantilever array with magnetic tuning including three piezoelectric bimorphs is investigated theoretically and experimentally. Other than harvester designs proposed before, this array is easy to manufacture and insensitive to manufacturi

Objectives: Serratia marcescens is a gram-negative pathogen of many species. The ability of S. marcescens to form biofilms and its potent innate resistance to antimicrobials and cleaning solutions are both essential for its pathogenicity and survival. The present study was conducted to investigate the effect of glyceryl trinitrate (GTN) on the biofilm of S. marcescens, as an alternative for antibiotic therapy. Methods: Different specimens, including ear swabs, burns, mid-stream urine, wound swabs, and sputum, were collected from patients who were brought to Al-Ramadi Hospital, Iraq. All samples were cultured, and the colonies that were obtained were detected using the VITEK® 2 compact. The ability of biofilms to develop was e

     This research Sought to identify the correlation relationships and the impact of each of the job description and perceived organizational support, Excellent Job performance of the heads of academic departments in the faculties of the University of Sulaymaniyah Iraqi Kurdistan Region, totaling (89) as President, and to achieve this was Default plan includes research variables as well as the formulation of a number of preparation fundamental assumptions, and researchers used a questionnaire for this purpose as a tool head of the collection of data and information, as it was distributed (80) copies, and the number of retrieved them (76) a copy of a valid statistical analysis, as well as conducting personal i

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

      Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

Business Ethics play a major role in explaining the behavior of those interested in the management of tourism enterprises in the field of management gains, which sometimes turn to manipulation in the specification of the service of tourism and influence in the technical characteristics at the expense of the brand and market share, as well as misleading beneficiaries about the fact that the performance of the service of tourism, may depend activities tourist dramatically when submitting and sharing various services on the types of mutual relations the framework for moral distinct, in interaction or direct contact between producers of tourism services and tourists or their beneficiaries, in order to provide comfort and recreation a