This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs  in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical exa

    In this paper, we present new algorithm for the solution of the second order nonlinear three-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions which are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of three point boundary value problems.

Research Summary
      Praise be to God, Lord of the worlds, and prayers and peace be upon the most honorable of the prophets and messengers, our master Muhammad, and on the good God and his righteous companions.
      For the most truthful hadith is the Book of God Almighty, and the best guidance is the guidance of the Prophet, may God bless him and grant him peace. If any)). Our good predecessor took care of collecting what they were able to collect and arrange from the words of the prophecy issued by our master Muhammad, peace and blessings be upon him, and wrote works on them including forms of support, parts, dictionaries, and mosques. About me, if any, in order to re

This work studies with produce of light fuel fractions of gasoline, kerosene and gas oil from treatment of residual matter that will be obtained from the solvent extraction process as by product from refined lubricate to improve oil viscosity index in any petroleum refinery. The percentage of this byproduct is approximately 10% according to all feed (crude oil) in the petroleum refinery process. The objective of this research is to study the effect of the residence time parameter on the thermal cracking process of the byproduct feed at a constant temperature, (400 °C). The first step of this treatment is the thermal cracking of this byproduct material by a constructed batch reactor occupied with control device at a selective range of re

This paper is focused on orthogonal function approximation technique FAT-based adaptive backstepping control of a geared DC motor coupled with a rotational mechanical component. It is assumed that all parameters of the actuator are unknown including the torque-current constant (i.e., unknown input coefficient) and hence a control system with three motor control modes is proposed: 1) motor torque control mode, 2) motor current control mode, and 3) motor voltage control mode. The proposed control algorithm is a powerful tool to control a dynamic system with an unknown input coefficient. Each uncertain parameter/term is represented by a linear combination of weighting and orthogonal basis function vectors. Chebyshev polynomial is used

Periodontal diseases are inflammatory diseases, for which, scaling and root planning is the main approach. Diode laser therapy as an adjunct to non-surgical periodontal treatment has shown some beneficial effects.

Aim: The objective of this single randomized controlled clinical study was to assess the effect of a 940 nm diode laser as an adjunct to SRP therapy in the treatment of periodontal pockets.

 Methods: In this study, twenty patients in need of periodontal treatment with periodontal pocket ≥ 4 mm were selected for this split-mouth clinical study. Test group treated by diode laser 940 nm as an adjunct with SRP, control group treated by SRP in contralateral quadrants. Clinical

Existence of these soils, sometimes with high gypsum content, caused difficult problems to the buildings and strategic projects due to dissolution and leaching of gypsum by the action of waterflow through soil mass. In this research, a new technique is adopted to investigate the performance of replacement and geosynthetic reinforcement materials to improve the gypseous soil behavior through experimential set up manufactured loaclally specially for this work. A series of tests were carried out using steel container (600*600*500) mm. A square footing (100*100) mm was placed at the center of the top surface of the bed soil. The results showed that the most effective thickness for the dune sand layer with geotextile at the interface, within

Background: Polymers are very rarely used in their form. These modifications are carried out in order to improve the properties of polymers.Recently silver have been used successfully as antimicrobial (medical and dental) biomaterials that can prevent caries and infection of implants Purposes: The aim of the present in vitro study is to evaluate the effect of addition of silver nitrate to acrylic resin in different concentrationsthrough several tests part of these are: The effect of this additive on impact strength, transverse strength, and tensile strength of AgNO3 – loaded resin, and to assess any effect of addition of silver nitrate on coloration of acrylic resin. Materials and methods: Different concentrations of silver nitrate

Abstract

In this work, diabetic glucose concentration level control under disturbing meal has been controlled using two set of advanced controllers. The first set is sliding mode controllers (classical and integral) and the second set is represented by optimal LQR controllers (classical and Min-, ax). Due to their characteristic features of disturbance rejection, both integral sliding mode controller and LQR Minmax controller are dedicated here for comparison. The Bergman minimal mathematical model was used to represent the dynamic behavior of a diabetic patient’s blood glucose concentration to the insulin injection. Simulations based on Matlab/Simulink, were performed to verify the performance of each controll

Extended calculations for  sputtering yield   through bombed Iron – target   by ( H,D ,T ,He )  ions plasma are accomplished .The calculations include changing the  input    parameters  :    the energy  of ( H,D ,T ,He ) ions plasma, the hit target angle of Iron, change  atomic   mass  of incident ion. The program TRIM is used to accomplish these calculations. The results     show   that   sputtering   yield is   directly   dependent   on   these parameters. It can   change the incident angle of ( H,D ,T ,He ) ions   and energy&n