This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

    This research includes the use of an artificial intelligence algorithm, which is one of the algorithms of biological systems which is the algorithm of genetic regulatory networks (GRNs), which is a dynamic system for a group of variables representing space within time. To construct this biological system, we use (ODEs) and to analyze the stationarity of the model we use Euler's method. And through the factors that affect the process of gene expression in terms of inhibition and activation of the transcription process on DNA, we will use TF transcription factors. The current research aims to use the latest methods of the artificial intelligence algorithm. To apply Gene Regulation Networks (GRNs), we used a progr

This study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All the previous is braced by theorems and examplesthat interpret the applicability and the firmness of the acquired provisions

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

Due to the importance of solutions of partial differential equations, linear, nonlinear, homogeneous, and non-homogeneous, in important life applications, including engineering applications, physics and astronomy, medical sciences, and life technology, and their importance in solutions to heat transfer equations, wave, Laplace equation, telegraph, etc. In this paper, a new double integral transform has been proposed.

In this work, we have introduced a new double transform ( Double Complex EE Transform ). In addition, we presented the convolution theorem and proved the properties of the proposed transform, which has an effective and useful role in dealing with the solution of two-dimensional partial differential equations. Moreover

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.