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.

A general velocity profile for a laminar flow over a flat plate with zero incidence is obtained by employing a new boundary condition to the other available boundary conditions. The general velocity profile is mathematically simple and nearest to the exact solution. Also other related values, boundary layer thickness, displacement thickness, momentum thickness and coefficient of friction are nearest to the exact solution compared with other corresponding values for other researchers.

The presented work shows a preliminary analytic method for estimation of load and pressure distributions on low speed wings with flow separation and wake rollup phenomena’s. A higher order vortex panel method is coupled with the numerical lifting line theory by means of iterative procedure including models of separation and wake rollup. The computer programs are written in FORTRAN which are stable and efficient.

      The capability of the present method is investigated through a number of test cases with different types of wing sections (NACA 0012 and GA(W)-1) for different aspect ratios and angles of attack, the results include the lift and drag curves, lift and pressure distributions along the wing s

Objective(s): assessment of  the health follow up and weight control for women with osteoporosis and find out the relationship between their health follow up and weight control and their socio-demographic characteristics.

Methodology: A descriptive study was conducted on women with osteoporosis for the period of September, 26^th 2020 to Jun, 20th 2021. Non- probability (convenient) sample of (70) women with osteoporosis selected from (5) Private Clinics for Joints and Fractures in Baqubah City. A questionnaire was designed though extensive review of literatures and it consists of three parts: the first part includes women’s socio demographic characteristics, the second part inclu

In this paper, the deterministic and the stochastic models are proposed to study the interaction of the Coronavirus (COVID-19) with host cells inside the human body. In the deterministic model, the value of the basic reproduction number   determines the persistence or extinction of the COVID-19. If   , one infected cell will transmit the virus to less than one cell, as a result,  the person carrying the Coronavirus will get rid of the disease .If   the infected cell  will be able to infect  all  cells that contain ACE receptors. The stochastic model proves that if  are sufficiently large then maybe  give  us ultimate disease extinction although ,  and this  facts also proved by computer simulation.

A linear and nonlinear theoretical and experimental aeroelastic investigation of a wing-flap-tab typical section model undergoing two-dimensional incompressible airflow is described. The linear flutter velocity (LFV) and frequency are predicted using linear analysis. Then a freeplay structural nonlinearity is considered in the tab. The structural equations of motion have been coupled with Theodorsen aerodynamic theory to produce the theoretical aeroelastic model which is analyzed by a state space method to predict the LFV and flutter frequency. Linear piecewise function has been used to introduce the tab spring stiffness in the freeplay state. The ground vibration test is used to measure the model structural dynamic characteristics. Then th

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimati