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.

The study aims to identify the impact of the round-robin strategy on the logical thinking of fourth-year middle school students in chemistry. Two groups were employed:  an experimental group consisted of (30) students who were taught according to the round-robin strategy, and the control group consisted of (30) students who were taught according to the traditional method. The researcher adopted the experimental design with partial control by preparing the visual thinking test tool, which consists of (20) multiple-choice items, it was applied as a post-test on the research sample. The result showed that there was a statistically significant difference in favor of the experimental group, which was taught according to the Round Robin s

solation of candida spp. From cancer patients who suffered oral candidiasis due to immunodeficiency

The main aim of this research study is to point out the vital importance of high-quality exterior audits to limit discretionary accounting, as it could distort a company’s commercial results. The research introduces a well-founded hypothesis on the preventive powers of high-quality audits, as it can act as a strong exterior control. The research focuses on testing the complex relationship between earnings management and investors’ behavior within the public-listed companies from the food industry. The research gathers credible annual comprehensive data from thirty-five publicly-listed firms from the United States. It encompasses the twenty years prior to 2024, as it includes the twenty years prior to 2024. Additionally, the gathered dat

After the information revolution that occurred in the Western world, and the developments in all fields, especially in the field of education and e-learning, from an integrated system based on the effective employment of information and communication technology in the teaching and learning processes through an environment rich in computer and Internet applications, the community and the learner were able to access information sources and learning at any time and place, in a way that achieves mutual interaction between the elements of the system and the surrounding environment. After the occurrence of the phenomenon of Covid 19, it led to a major interruption in all educational systems that had never happened before, and the disrupt

eclaration has become today has an important and active and influential role in the recipient public life، and are concentrated advertising on the creativity component manufacture to attract his attention toward what to be announced from a variety products ، and is dominated by television commercials tempo and imagination، and display them a variety of ways catches the attention and an impressive simulates the their senses of hearing and sight ، to influence in the receiver and the public paid for purchase. Through it crystallization the subject of our research on the importance of creativity in television advertising and effective for attracting the attention of the public towards the receiver advertised products، and in

The gamma dose rates and specific activity of 137Cs, 60Co and 40K in
samples of soil taken from places near the landfill radiation at Al-
Tuwaitha site were measured using a portable NaI(Tl) detector. The
results of gamma dose rates in samples were ranged from 52.6
nGy.h-1 to 131nGy.h-1. Then the specific activity of 137Cs, 60Co and
40K in soil were determined using high pure germanium (HPGe)
detector. The specific activities were varied from 1.9 to 115500 Bq.
kg-1 for 137Cs, from 6.37 to 616.5 Bq. kg-1 for 60Co, and from 3 to
839.5 Bq. kg-1 for 40K. The corresponding health risk for the annual
effective dose equivalent varied from 1.85×10-14 to 15.7mSv/y. The
results were compared with various internationa