In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.

     Fractional calculus has paid much attention in recent years, because it plays an essential role in many fields of science and  engineering, where the study of stability theory of fractional differential equations emerges to be very important. In this paper, the stability of fractional order ordinary differential equations will be studied and introduced the backstepping method. The Lyapunov function  is easily found by this method. This method also gives a guarantee of stable solutions for the fractional order differential equations. Furthermore it gives asymptotically stable.

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

Recently Genetic Algorithms (GAs) have frequently been used for optimizing the solution of estimation problems. One of the main advantages of using these techniques is that they require no knowledge or gradient information about the response surface. The poor behavior of genetic algorithms in some problems, sometimes attributed to design operators, has led to the development of other types of algorithms. One such class of these algorithms is compact Genetic Algorithm (cGA), it dramatically reduces the number of bits reqyuired to store the poulation and has a faster convergence speed. In this paper compact Genetic Algorithm is used to optimize the maximum likelihood estimator of the first order moving avergae model MA(1). Simulation results

In recent years, due to the economic benefits and technical advances of cloud
computing, huge amounts of data have been outsourced in the cloud. To protect the
privacy of their sensitive data, data owners have to encrypt their data prior
outsourcing it to the untrusted cloud servers. To facilitate searching over encrypted
data, several approaches have been provided. However, the majority of these
approaches handle Boolean search but not ranked search; a widely accepted
technique in the current information retrieval (IR) systems to retrieve only the top–k
relevant files. In this paper, propose a distributed secure ranked search scheme over
the encrypted cloud servers. Such scheme allows for the authorized user to

The water vapor is one of the constituent elements of the rain and the superiority
of its importance in the study of climate because it is the basis on which depends all
the different aspects of condensation. The purpose of research is to analyze the time
series of the Baghdad station andan analyze these series to see whether there is a
relationship between these two variables. Obtained the data used in this research
from the National Center for Environmental Prediction for the period from 1948 to
2011. The use of statistical criteria included linear regression and Mann Kandal test
to find the link. The results of time series monthly presence decrease in rainfall and
all months except October, either the results o

This article addresses a new numerical method to find a numerical solution of the linear delay differential equation of fractional order , the fractional derivatives described in the Caputo sense. The new approach is to approximating second and third derivatives. A backward finite difference method is used. Besides, the composite Trapezoidal rule is used in the Caputo definition to match the integral term. The accuracy and convergence of the prescribed technique are explained. The results  are shown through numerical examples.