In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

This paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

 A simulation study is used to examine the robustness of some estimators on a multiple linear regression model with problems of multicollinearity and non-normal errors, the Ordinary least Squares (LS) ,Ridge Regression, Ridge Least Absolute Value (RLAV), Weighted Ridge (WRID), MM and a robust ridge regression estimator MM estimator, which denoted as RMM this is the modification of the Ridge regression by incorporating robust MM estimator . finialy, we show that RMM is the best among the other estimators

This study relates to  the estimation of  a simultaneous equations system for the Tobit model where the dependent variables  ( )  are limited, and this will affect the method to choose the good estimator. So, we will use new estimations methods  different from the classical methods, which if used in such a case, will produce biased and inconsistent estimators which is (Nelson-Olson) method  and  Two- Stage limited dependent variables(2SLDV) method  to get of estimators that hold characteristics the good estimator .

That is , parameters will be estim

In the present study, an attempt has been made to study the change in water quality of the river in terms of turbidity during lockdown associated with COVID-19. Iraq announced the longest-ever lockdown on 25 March 2020 due to COVID-19 pandemic. 

In the absence of ground observations, remote sensing data was adopted, especially during this period. The change in the visible region's spectral reflectance of water in part of the river has been analyzed using the Landsat 8 OLI multispectral remote sensing data at Tigris River, Salah al-Din province (Bayji / near the refinery), Iraq. It was found that the green and red bands are most sensitive and can be used to estimate turbidity. Furthermore, the temporal variation in turbidity was a

In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)

The pandemic of coronavirus disease 2019 (COVID-19), first reported in China, in December 2019 and since then the digestive tract involvement of  COVID-19 has been progressively described. In this review, I summed recent studies, which have addressed the pathophysiology of COVID-19-induced gastrointestinal symptoms, their prevalence, and bowel pathological and radiological findings of infected patients. The effects of gut microbiota on SARS-CoV-2 and the challenges of nutritional therapy of the infected patients are depicted.  Moreover, I provide a concise summary of the recommendations on the management of inflammatory bowel disease, colorectal cancer, and performing endoscopy in the COVID era. Finally, the COVID pancreatic re