In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

In this study, we used Bayesian method to estimate scale parameter for the normal distribution. By considering three different prior distributions such as the square root inverted gamma (SRIG) distribution and the non-informative prior distribution and the natural conjugate family of priors. The Bayesian estimation based on squared error loss function, and compared it with the classical estimation methods to estimate the scale parameter for the normal distribution, such as the maximum likelihood estimation and th

The goal of our study is to perform detailed multiband surface photometry of the spiral galaxy NGC 4448 and its brightest star-forming regions. The structure and composition of the stellar population in the surface brightness galaxy NGC 4448 was studied using BVR CCD photometry. The observations were obtained on the 1.88 m optical telescope of Kottamia Astronomical Observatory (KAO), Egypt. A two-dimensional decomposition of the galaxy bulge and disk components is carried out. A powerful star forming region is observed near the galactic center. Based on the positions of the various components of the galaxy in two color diagrams. From the observations, the surface brightness profiles, Ellipticity profiles, position angle profiles and colo

In this research study failed Annunciation No. 10 for the fourth phase of the pressure of carbon dioxide of the company for Southern Fertilizers and repeated the failures more than once for the same gospel was a detailed study of the gospel included a series tests for properties Mechanical and Structural addition to the tests microscopic and scanning electron microscope shows m This study parameters and a failure Elal well as the existence of an old internal cracks in the metal of the Annunciation

In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

Glass Fiber Reinforced Polymer (GFRP) beams have gained attention due to their promising mechanical properties and potential for structural applications. Combining GFRP core and encasing materials creates a composite beam with superior mechanical properties. This paper describes the testing encased GFRP beams as composite Reinforced Concrete (RC) beams under low-velocity impact load. Theoretical analysis was used with practical results to simulate the tested beams' behavior and predict the generated energies during the impact loading. The impact response was investigated using repeated drops of 42.5 kg falling mass from various heights. An analysis was performed using accelerometer readings to calculate the generalized inertial load. The in

The services provided by the municipal institutions of the basic things needed by the man in his daily life and the evolution of cities basically depends on these services and therefore has paid most of the world's attention to this vital facility and give him the biggest concern for the welfare of the citizens, as is the research problem that there is no program scrutiny to evaluate the performance of municipal institutions contribute to measuring the efficiency and effectiveness of the services provided and was based on research on the premise that the preparation of the existence of audit program to evaluate the performance of municipal institutions contribute to measuring the efficiency and effectiveness of services provided has reac

This paper aimed to test random walking through the ISX60 market index for the ability to judge market efficiency at a weak level. The study used Serial Correlation Test, the Runs Test, the Variance Ratio Test, as well as the Rescaled Range Test.The population of the study represents of Iraq Stock Exchange. The study concluded accepting the hypothesis of the study that the returns of the ISX60 market index in the Iraqi market for securities does not follow the random walking in general and as a result the Iraq market for securities is inefficient within the weak level of efficiency and the study recommended need a supervisors work in the Iraqi market for securities to activate all means a which will work to communication with information

One of the challenging issues encountered during drilling operations is the lost circulation. Numerous issues might arise because of losses, such as wasting of time and higher drilling cost. Several types of lost circulation materials have been developed and are being used to limit mud losses and avoid associated issues. Each solution has benefits and drawbacks.

In this study, a core flooding test was performed to study the effectiveness of polyacrylamide (PAM) granular gel on the reduction of the circulation lost. One common type of fracture characteristic is fractures with tips, commonly known as partially open fracture (POF). However, PAM gel therapy in POFs received little attention in prior research. Models of partly open fra