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.

Recently, new generalizations have been presented for the hyponormal operators, which are (N, k)-hyponormal operators and (h, M)-hyponormal operators. Some properties of these concepts have also been proved, one of these properties is that the product of two (N, k)-hyponormal operator is also (N, k)- hyponormal operator and the product of two (h, M)-hyponormal operators is (h, M)-hyponormal operator. In our research, we will reprove these properties by using the (l,m)-commuting operator equations, in addition to that we will solve the (l, m)-commuting operator equations for (N, k)-hyponormal operators and (h, M)-hyponormal operators.

This paper includes the estimation of the scale parameter of weighted Rayleigh distribution using well-known methods of estimation (classical and Bayesian). The proposed estimators were compared using Monte Carlo simulation based on mean squared error (MSE) criteria. Then, all the results of simulation and comparisons were demonstrated in tables. 

Computations of the relative permeability curves were made through their representation by two functions for wetting and nonwetting phases. Each function contains one parameter that controls the shape of the relative permeability curves. The values of these parameters are chosen to minimize an objective function, that is represented as a weighted sum of the squared differences between experimentally measured data and the corresponding data calculated by a mathematical model simulating the experiment. These data comprise the pressure drop across core samples and the recovery response of the displacing phase. Two mathematical models are constructed in this study to simulate incompressible, one-dimensional, two-phase flow. The first model d

         In the present paper, the authors introduce and investigates two new subclasses and,  of the class k-fold bi-univalent functions in the open unit disk. The initial coefficients for all of the functions that belong to them were determined, as well as the coefficients for functions that belong to a field determining these coefficients requires a complicated process. The bounds for the initial coefficients and are contained among the remaining results in our analysis are obtained. In addition, some specific special improver results for the related classes are provided.

This research represents a reflection seismic study (structural and stratigraphic) for a (852) km2 area located in the south of Iraq within the administrative border of the province of Al-Muthanna and Qadisiyah province ,by using 2-D seismic data from Oil Exploration company three main seismic reflectors are picked, these are (Zubair and Yamama) Formations which they deposited during the Cretaceous age , and (Gotnia) Formation which deposited during Jurassic age .Structural maps of Formations are prepared to obtain the location and direction of the sedimentary basin and shoreline ,time, velocity and depth maps are drawn depending on the structural interpretation of the picked reflectors and show several structural feature as nose structu

Ping message focused on highlighting the fact commodity trading in Iraq, and increased exposure to world merchandise trade imbalance, which dominate Iraq's foreign trade major commodity is oil, and therefore the inability of Iraq to control financial revenue as a result of the fluctuations in the international market, the shortage of commodity products will lead inevitably to the weakness in the ability of the local market to meet the internal demand and due to the lack of flexible production machine For agricultural, industrial and economic sectors are responding to changes in the domestic or external demand which will open the door to merchandise imports to invade these markets, since the adoption of the Iraq oil exports,

This paper discusses an optimal path planning algorithm based on an Adaptive Multi-Objective Particle Swarm Optimization Algorithm (AMOPSO) for two case studies. First case, single robot wants to reach a goal in the static environment that contain two obstacles and two danger source. The second one, is improving the ability for five robots to reach the shortest way. The proposed algorithm solves the optimization problems for the first case by finding the minimum distance from initial to goal position and also ensuring that the generated path has a maximum distance from the danger zones. And for the second case, finding the shortest path for every robot and without any collision between them with the shortest time. In ord

The  thermal  and  electrical  performance  of  different  designs  of  air  based  hybrid photovoltaic/thermal collectors is investigated experimentally and theoretically. The circulating air is used to cool PV panels and to collect the absorbed energy to improve their performance. Four different collectors have been designed, manufactured and instrumented namely; double PV panels without cooling (model I), single duct double pass collector (model II), double duct single pass (model III), and single duct single pass (model IV) . Each collector consists of: channel duct, glass cover, axial fan to circulate air and two PV panel in parallel connection. The temperature of the upper and

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.