In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall

     In this article, the lattice Boltzmann method with two relaxation time  (TRT)  for the  D2Q9 model is used to investigate numerical results for 2D flow. The problem is performed to show the dissipation of the kinetic energy rate and its relationship with the enstrophy growth for 2D dipole wall collision. The investigation is carried out for normal collision and oblique incidents at an angle of . We prove the accuracy of moment -based boundary conditions with slip and Navier-Maxwell slip conditions to simulate this flow. These conditions are under the effect of Burnett-order stress conditions that are consistent with the discrete Boltzmann equation. Stable results are found by using this kind of boundary condition where d

In this research, optical communication coding systems are designed and constructed by utilizing Frequency Shift Code (FSC) technique. Calculations of the system quality represented by signal to noise ratio (S/N), Bit Error Rate (BER),and Power budget are done. In FSC system, the data of Nonreturn- to–zero (NRZ ) with bit rate at 190 kb/s was entered into FSC encoder circuit in transmitter unit. This data modulates the laser source HFCT-5205 with wavelength at 1310 nm by Intensity Modulation (IM) method, then this data is transferred through Single Mode (SM) optical fiber. The recovery of the NRZ is achieved using decoder circuit in receiver unit. The calculations of BER and S/N for FSC system a

Wind energy is one of the most common and natural resources that play a huge role in energy sector, and due to the increasing demand to improve the efficiency of wind turbines and the development of the energy field, improvements have been made to design a suitable wind turbine and obtain the most energy efficiency possible from wind. In this paper, a horizontal wind turbine blade operating under low wind speed was designed using the (BEM) theory, where the design of the turbine rotor blade is a difficult task due to the calculations involved in the design process. To understand the behavior of the turbine blade, the QBlade program was used to design and simulate the turbine rotor blade during working conditions. The design variables suc

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

This paper demonstrates the construction designing analysis and control strategies for fully tracking concentrated solar thermal by using programmable logic control in the city of Erbil-Iraq. This work used the parabolic dish as a concentrated solar thermal. At the focal point, the collected form of energy is used for heating a (water) in the receiver, analyzing this prototype in real-time with two different shapes of the receiver and comparing the results. For tracking the parabolic dish, four light-dependent resistors are used to detect the sun's position in the sky so that the tracking system follows it to make the beam radiation perpendicular to the collector surface all of the time during the day for maximum solar p