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.

Background: The risk of antibiotics resistance (AR) increases due to excessive of antibiotics either by health care provider or by the patients.

Objective: The assessment of the self-medication Practice of over the counter drugs and other prescription drugs and its associated risk factor.

Subjects and Methods: Study design: A descriptive study was conducted from “20th December 2019 to 08th January 2021”. A pre validated and structured questionnaire in English and Urdu language was created to avoid language barrier including personal detail, reasons and source and knowledge about over the counter drugs and Antibiotics. Sample of the study was randomly selected.

Buried pipeline systems are commonly used to transport water, sewage, natural oil/gas and other materials. The beneficial of using geogrid reinforcement is to increase the bearing capacity of the soil and decrease the load transfer to the underground structures.

This paper deals with simulation of the buried pipe problem numerically by finite elements method using the newest version of PLAXIS-3D software. Rajkumar and Ilamaruthi's study, 2008 has been selected to be reanalyzed as 3D problem because it is containing all the properties needed by the program such as the modulus of elasticity, Poisson's ratio, angle of internal friction. It was found that the results

Nutrient enrichment of Sawa lake water was made using different nitrogen and phosphorus concentrations during autumn and spring at three stations. Different concentrations of nitrogen, phosphorus and N: P ratios were used to test variations in phytoplankton population dynamics. Nitrogen at a concentration of 25 µmole.l-1 and N: P ratio of 10:1 gave highest phytoplankton cell number at all stations and seasons. A total of 64 algal taxa dominated by Bacillariophyceae followed by Cyanophyceae and Chlorophyceae were identified. The values of Shannon index of diversity were more than one in the studied stations.

The oil exports play a vital role in supporting economic development and raise the economic growth. The oil exports can increase the economic growth via three main channels which are supporting the productive, distributive and service sectors; increasing the investment and capital formation; and increasing the employment rate.

However, the oil exports did not have an important role in increasing the economic growth in Iraq. Therefore, it also did not provide the required support to other economic sectors, neither participated in increase the employees’ skills nor increase the investment rate. It may slightly contribute in enhancement the infrastructure that can attract the public and private investments

The aim of the research is to estimate the hidden population. Here، the number of drug users in Baghdad was calculated for the male age group (15-60) years old ، based on the Bayesian models. These models are used to treat some of the bias in the Killworth method Accredited in many countries of the world.

Four models were used: random degree، Barrier effects، Transmission bias، the first model being random، an extension of the Killworth model، adding random effects such as variance and uncertainty Through the size of the personal network، and when expanded by adding the fact that the respondents have different tendencies، the mixture of non-random variables with random to produce

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc

Non-additive measures and corresponding integrals originally have been introduced by Choquet in 1953 (1) and independently defined by Sugeno in 1974 (2) in order to extend the classical measure by replacing the additivity property to non-additive property. An important feature of non –additive measures and fuzzy integrals is that they can represent the importance of individual information sources and interactions among them. There are many applications of non-additive measures and fuzzy integrals such as image processing, multi-criteria decision making, information fusion, classification, and pattern recognition. This paper presents a mathematical model for discussing an application of non-additive measures and corresp