This paper deals with finding an approximate solution to the index-2 time-varying linear differential algebraic control system based on the theory of variational formulation. The solution of index-2 time-varying differential algebraic equations (DAEs) is the critical point of the equivalent variational formulation. In addition, the variational problem is transformed from the indirect into direct method by using a generalized Ritz bases approach. The approximate solution is found by solving an explicit linear algebraic equation, which makes the proposed technique reliable and efficient for many physical problems. From the numerical results, it can be implied that very good efficiency, accuracy, and simplicity of the pre

In this paper, we model the spread of coronavirus (COVID -19) by introducing stochasticity into the deterministic differential equation susceptible  -infected-recovered (SIR model). The stochastic SIR dynamics are expressed using Itô's formula. We then prove that this stochastic SIR has a unique global positive solution I(t).The main aim of this article is to study the spread of coronavirus COVID-19 in Iraq from 13/8/2020 to 13/9/2020. Our results provide a new insight into this issue, showing that the introduction of stochastic noise into the  deterministic model for the spread of COVID-19 can cause the disease to die out, in scenarios where deterministic models predict disease persistence. These results were also clearly ill

     In this paper, the oscillatory properties and asymptotic behaviour of a third-order three-dimensional neutral system are discussed.  Some sufficient conditions are obtained to ensure that all bounded positive solutions of the system are oscillatory or non-oscillatory.  On the other hand, the non-oscillatory solutions either converge or diverge when  goes to infinity. A special technique is adopted to include all possible cases. The obtained results include illustrative examples.

The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

 A dynamic analysis method has been developed to investigate and characterize embedded delamination on the dynamic response of composite laminated structures. A nonlinear finite element model for geometrically large amplitude free vibration intact plate and delamination plate analysis is presented using higher order shear deformation theory where the nonlinearity was introduced  in the Green-Lagrange sense. The governing equation of the vibrated plate were derived using the Variational approach. The effect of different orthotropicity ratio, boundary condition and delamination size on the non-dimenational fundamental frequency and frequency ratios of plate for different stacking sequences are studied. Finally th

We extended the characterization of strict local minimizers of order two in ward,s
theorem for nonlinear problem to a certain class of nonsmooth semi-infinite problems with inequality constraints in the nonparametric constraint case.

In this work, we are concerned with how to find an explicit approximate solution (AS) for the telegraph equation of space-fractional order (TESFO) using Sumudu transform method (STM). In this method, the space-fractional order derivatives are defined in the Caputo idea. The Sumudu method (SM) is established to be reliable and accurate. Three examples are discussed to check the applicability and the simplicity of this method. Finally, the Numerical results are tabulated and displayed graphically whenever possible to make comparisons between the AS and exact solution (ES).

Several efforts have been made to study the behavior of Total Electron Content (TEC) with many types of geomagnetic storm, the purpose of this research is to study the disturbances of the ionosphere through the TEC parameter during strong, severe and great geomagnetic storms and the validity of International Reference Ionosphere IRI model during these kinds of storms. TEC data selected for years 2000-2013 (descending solar cycle 23 to ascending cycle 24), as available from koyota Japan wdc. To find out the type of geomagnetic storms the Disturbance storm time (Dst) index was selected for the years (2000-2013) from the same website. Data from UK WDC have been taken for the solar indices sunspots number (SSN), radio flux (F10.7) and ionosp

Accurate description of thermodynamic, structural, and electronic properties for bulk and surfaces of ceria (CeO₂) necessitates the inclusion of the Hubbard parameter (U) in the density functional theory (DFT) calculations to precisely account for the strongly correlated 4f electrons. Such treatment is a daunting task when attempting to draw a potential energy surface for CeO₂-catalyzed reaction. This is due to the inconsistent change in thermo-kinetics parameters of the reaction in reference to the variation in the U values. As an illustrative example, we investigate herein the discrepancy in activation and reaction energies for steps underlying the partial and full hydrogenation of acetyl

In this study, the magic nuclei is divided into two groups, one of them is light group and the other is middle group, it was calculated shell corrections for all nuclei, and also it was concluded the relationship between cross sections for nuclear reactions ()α,n and the mass number (A) for all nuclei to incident neutrons (14.5 MeV). We found empirical equations to asymmetry parameter (N-Z)/A as function of mass number and for that two groups: for A=38 to A=40 light nuclei.()0534.10263.0+−=−AAZN for A=50 to A=89 middle nuclei. ()408.00151.00001.02−+=−AAAZN for A=90 to A=144 middle nuclei. ()0711.10221