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.

Flexible pavements are considered an essential element of transportation infrastructure. So, evaluations of flexible pavement performance are necessary for the proper management of transportation infrastructure. Pavement condition index (PCI) and international roughness index (IRI) are common indices applied to evaluate pavement surface conditions. However, the pavement condition surveys to calculate PCI are costly and time-consuming as compared to IRI. This article focuses on developing regression models that predict PCI from IRI. Eighty-three flexible pavement sections, with section length equal to 250 m, were selected in Al-Diwaniyah, Iraq, to develop PCI-IRI relationships. In terms of the quantity and severity of eac

Background: Celiac disease is an autoimmune chronic disease that affects the human’s intestine and subsequently reflects its effect on the entire body health by retardation the absorption and immune mediated complications cause the involvement of oral health. The present study intended to evaluate the impact of the histopathological disease activity upon dental enamel defects and dental caries.

Subjects and methods: Forty celiac-diseased patients aged 7-11 years were collected from 3 different teaching hospitals in Baghdad classified by means of the histopathological activity of the intestinal disease according to modified Marsh-Ros

This paper proposes a neuro-fuzzy system to model β-glucosidase activity based on the reaction’s pH level and temperature. The developed fuzzy inference system includes two input variables (pH level and temperature) and one output (enzyme activity). The multi-input fuzzy inference system was developed in two stages: first, developing a single input-single output fuzzy inference system for each input variable (pH, temperature) separately, using the robust adaptive network-based fuzzy inference system (ANFIS) approach. The neural network learning techniques were used to tune the membership functions based on previously published experimental data for β-glucosidase. Second, each input’s optimized membership functions from the ANF