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.

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

Braces in straight bridge systems improve the lateral-torsional buckling resistance of the girders by reducing the unbraced length, while in horizontally curved and skew bridges, the braces are primary structural elements for controlling deformations by engaging adjacent girders to act as a system to resist the potentially large forces and torques caused by the curved or skewed geometry of the bridge. The cross-frames are usually designed as torsional braces, which increase the overall strength and stiffness of the individual girders by creating a girder system that translates and rotates as a unit along the bracing lines. However, when they transmit the truck’s live load forces, they can produce fatigue cracks at their connection

           English has for long been one of the most widely used media of communication globally, especially in the Malaysian universities. It has been termed as a Lingua Franca because it is shared with other languages which are considered first languages by different speakers. For this reason, English as a Lingua Franca (ELF) has attracted a number of researchers to investigate its variety via other languages in various communities. The objective of this paper is therefore to establish the strategies which are employing by the international students at the National University of Malaysia/ UniversitiKebangsaan Malaysia (UKM) as an example of one of the Malaysian universities; when they e

This study came for the reason that some project administrations still do not follow the appropriate scientific methods that enable them to perform their work in a manner that achieves the goals for which those projects arise, in addition to exceeding the planned times and costs, so this study aims to apply the methods of network diagrams in Planning, scheduling and monitoring the project of constructing an Alzeuot intersection bridge in the city of Ramadi, as the research sample, being one of the strategic projects that are being implemented in the city of Ramadi, as well as being one of the projects that faced during its implementation Several of problems, the project problem was studied according to scientific methods through the applica

Preparing teacher occupies the attention of many thinkers and philosophers since the age of
kaldinics ( people of mesoptam / 2342 pH ) to the Islamic age where moslems philosophers
focus their attention on thought and philosophy where the philosophy of that teaching
depends on : teacher , student and family begin .
So , the issue of preparing and training teacher occupies the attention of education scientists
depending on his vital and important role in implementing of teaching policies in philosophies
and Islamic educational thought , therefore , the preparing and development of the teacher
regards as one of the basics of teaching development because of its importance in
development of teaching performance and th

This study showed that the lens in baloot muluki fish Chondrostoma regium is transparent, spherical shape, and solid in textures, while in the tree frog Hyla arborea savignyi, freshwater turtles Clemmys caspia caspia, white–eared bulbul Pycnonotus leucotis and brown rat Rattus norvegicus are transparent, soft and biconvex, it is very soft in white–eared bulbul. There are many significant differences have been recorded between the average weight lens and the total concentration of the protein in the lens all studied animals. Electrical migration process for lens proteins showed that there is one bundle of crystalline –? and one bundle also crystalline–? in all studied species, either crystalline–? may represent one bundle character

Introduction: Articaine was developed in 1969, with reported advantages which are increased potency, increased duration of its anesthetic effect and superior diffusion through bony tissue. The effectiveness of using 4% articaine infiltration for extraction of mandibular molar teeth in comparison to 2% lidocaine inferior alveolar nerve block is not settled yet. Aim: The aim of this study was to evaluate the effectiveness of using 4% articaine infiltration for extraction of mandibular molars by comparing it to the use of 2% lidocaine inferior alveolar nerve block in terms of success, the volume of local anesthetic agents and the pain experienced during the procedure. Materials and methods: A prospective randomized controlled study included

Negotiation is considered as one of the most important kinds of communication in the contemporary organizations, which depend on the important role of managerial information systems in providing necessary and suitable information for success of the negotiation process.

Accordingly, this study aims at measuring the extent of the variables effect of managerial information system in the negotiation process.

To achieve this study, two hypotheses were chosen; the first is the correlation relation and the second is the effect, and statistical means represented by correlation coefficient "Spearman" and (R²) were used.

 A Number of conclusions were