We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

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.

The main purpose of this paper, is to characterize new admissible classes of linear operator in terms of seven-parameter Mittag-Leffler function, and discuss sufficient conditions in order to achieve certain third-order differential subordination and superordination results. In addition, some linked sandwich theorems involving these classes had been obtained.  

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

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.

The control of water represents the safe key for fair and optimal use to protect water resources due to human activities, including untreated wastewater, which is considered a carrier of a large number of antibiotic-resistant bacterial species. This study aimed to investigate the prevalence of antibiotic-resistance to E. coli in Tigris River by the presence of resistance genes for aminoglycoside(qepA( ,quinolone (gyrA), and sulfa drugs( dfr1 ,dfr17) due to the frequent use of antibiotics and their release into wastewater of hospitals. Samples were collected from three sites on Tigris River: S1( station wastewater in Adhamiya), S2 (station wastewater in Baghdad Medical city hospital), S3 (station wastew

BCl3 is toxic gas and its detection is of great importance. Thus, here, B3LYP, M06-2X, and B97D density functionals are utilized for probing the effect of decorating Zn, Cd, and Au on the sensing performance of an AlP nano-sheet (AlPNS) in detecting the BCl3. We predict that the interaction of pure AlPNS with BCl3 is physisorption, and the sensing response (SR) of AlPNS is approximately 9.2. The adsorption energy of BCl3 changes from −4.1 to −18.8, −19.1, and −19.5 kcal/mol by decorating the Zn, Cd, and Au metals into the AlPNS surface, respectively. Also, the corresponding SR meaningfully rises to 40.4, 59.0, and 80.9, indicating that by increasing the atomic number of metals, the sensitivity of metal decorated AlPNS (metal@AlPNS)