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 paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

Maintaining and breeding fish in a pond are a crucial task for a large fish breeder. The main issues for fish breeders are pond management such as the production of food for fishes and to maintain the pond water quality. The dynamic or technological system for breeders has been invented and becomes important to get maximum profit return for aquaponic breeders in maintaining fishes. This research presents a developed prototype of a dynamic fish feeder based on fish existence. The dynamic fish feeder is programmed to feed where sensors detected the fish's existence. A microcontroller board NodeMCU ESP8266 is programmed for the developed h

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

The main idea of this paper is to define other types of a fuzzy local function and study the advantages and differences between them in addition to discussing some definitions of finding new fuzzy topologies. Also in this research, a new type of fuzzy closure has been defined, where the relation between the new type and different types of fuzzy local function has been studied

Each book has a specific style in which its author walks on it from its beginning to its end, and the Holy Qur’an is a book that compiled many methods that were indicative of its miracle, and that it is one unit even though it has been astrologer for twenty-three years.
There is no doubt that knowledge of the Qur’anic methods is one of the pillars of the approach that deals with any of the Qur’an, and the multiplicity of Qur’anic methods is a fact that has many causes. It has been expressed by the Qur’anic discharge and the conjugation of verses to bring them to different methods, and on multiple forms such as nominal, actual, singular Qur’an, presentation, delay, deletion, mention, abbreviation and redundancy. The Qur'ani

During the two last decades ago, audio compression becomes the topic of many types of research due to the importance of this field which reflecting on the storage capacity and the transmission requirement. The rapid development of the computer industry increases the demand for audio data with high quality and accordingly, there is great importance for the development of audio compression technologies, lossy and lossless are the two categories of compression. This paper aims to review the techniques of the lossy audio compression methods, summarize the importance and the uses of each method.