The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

     The increase in military spending has become a feature of the times for many countries, including China. They have sought to increase their defence spending, not with the aim of domination and possession, but rather to protect their economic interests and to secure their foreign trade. The research aims to identify the impact of military spending by studying the nature of defence spending and its role in providing security. And stability and facilitating foreign investment in it, as well as storming the military industry, securing some humanitarian supplies, and participating in a variety of public works that can be used in the civil and military fields, and the aim of the research is to id

In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

A field experiment was conducted at the experimental field of botanical garden, faculty of science, university of Baghdad, in order to study the effect of plant density on growth and yield of two local cultivars of sunflower (Sin Althieb and Shumose). The densities used were 4.4 and 8.8 plant/m². The results showed difference between cultivars in their agronomic traits and their yields. There was a significant increase in plant height and leaf area index by increasing the plant density, while head diameter, number of seeds and leaf area decreased. But the most significant effect was the increasing in yield and biological yield by increasing the plant density. There was an increase by 72% and 58% in the yield and 79% an

This research is concerned with the study of (the aesthetic of constructive relations in linear composition) with what distinguished Arabic calligraphy through the style and artistic method in its construction, and the specifications it carries that enabled it to pay attention to building formations to achieve in its total linear ranges aesthetic values and relationships. Through the research, the models and the exploratory study that he obtained, the researcher was able to raise the research problem in the first chapter according to the following question: What is the aesthetic of constructive relations in linear formation?
The importance of the research in achieving the aesthetics of the formations, which is a wide field according t

The aim of this paper is to present a weak form of -light functions by using -open set which is -light function, and to offer new concepts of disconnected spaces and totally disconnected spaces. The relation between them have been studied. Also, a new form of -totally disconnected and inversely -totally disconnected function have been defined, some examples and facts was submitted.

This paper introduces a Certain Subclass of Meromorphic Univalent Positives Coefficients Defined by the q-Difference Operator. Coefficient estimates are investigated and obtained, and the upped bound is calculated.

In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd 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 methods i

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact