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 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 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.

       In this paper, we apply a new technique combined by a Sumudu transform and iterative method called the Sumudu iterative method for resolving non-linear partial differential equations to compute analytic solutions. The aim of this paper is to construct the efficacious frequent relation to resolve these problems. The suggested technique is tested on four problems. So the results of this study are debated to show how useful this method is in terms of being a powerful, accurate and fast tool with a little effort compared to other iterative methods.

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

       In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.

     In this paper, new integro-differential operators are introduced that defined by Salagean’s differential operator. The major object of the present study is to investigate convexity properties on new geometric subclasses included these new operators.

This research deals with the study of pathways in terms of the negative effect in proving them
And the fact of this influence among fundamentalists.
The research consists of two subjects and a conclusion.
In the first section, I learned about the terms in the title of the research:
Denial and pathology.
In the second section I reviewed the pathways of illness that affect exile in it
Five: the nodding, the fitting, the sounding, the division, the rotation, the inference
A description of the absence of evidence of non-reference to it. And I figured out how
Negation in it by striking some illustrative examples as fruit
Arising from the effect of negation in proving those routes.
As a result of this research, a

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.