This paper applies the Modified Adomian Decomposition Method (MADM) for solving Integro-Differential Inequality, this method  is one of effective to construct analytic approximate solutions for linear and nonlinear integro-differential inequalities without solving many integrals and transformed or discretization. Several examples are presented, the analytic results show that this method is a promising and powerful for solving these problems.

The present work aims to study forward osmosis process using different kinds of draw solutions and membranes. Three types of draw solutions (sodium chloride, sodium formate, and sodium acetate) were used in forward osmosis process to evaluate their effectiveness with respect to water flux and reverse salt flux. Experiments conducted in a laboratory-scale forward osmosis (FO) unit in cross flow flat sheet membrane cell.  Three types of membranes (Thin film composite (TFC), Cellulose acetate (CA), and Cellulose triacetate (CTA)) were used to determine the water flux under osmotic pressure as a driving force. The effect of temperature, draw solution concentration, feed and draw solution flow rate, and membrane types, were studied with

      The research aims to study the corrosion of aluminum alloy(6061) in 0.6 mol. dm^-3 NaCl solution in base medium  was examined with out and with Gallic acid as environmentally – friendly corrosion inhibitor at temperature range (298-313)K. The inhibitive action of gallic acid on corrosion of aluminum alloy(6061)  in KOH solution was examined through electrochemical polarization method using potentiostatic technique and surface analysis by optical microscopy,  Polarization measurements indicate that the examined compound act as a mixed type inhibitor. Results appeared that the inhibition occurs through adsorption of the inhibitor molecules on the metal surface and it was obeyed

An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has

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

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.

The present work describes guggul as a novel carrier for some anti-inflammatory drugs. Guggulusomes containing different concentration of guggul with aceclofenac were prepared by sonication method and characterized for vesicle shape, size, size-distribution, pH, viscosity, spread ability, homogeneity, and accelerated stability in-vitro drug permeation through mouse skin. The vesicles exhibited an entrapment efficiency of 93.2 ± 12%, vesicle size of 0.769 ± 3μm and a zeta potential of - 6.21mV. In vitro drug release was analyzed using Franz’s diffusion cells. The cumulative release of the guggulusomes gel (G2) was 75.8% in 18 hrs, which is greater than that all the gel formulation. The stability profile of prepare

    In this paper, we studied the scheduling of  jobs on a single machine.  Each of n jobs is to be processed without interruption and becomes available for processing at time zero. The objective is to find a processing order of the jobs, minimizing the sum of maximum earliness and maximum tardiness. This problem is to minimize the earliness and tardiness values, so this model is equivalent to the just-in-time production system. Our lower bound depended on the decomposition of the problem into two subprograms. We presented a novel heuristic approach to find a near-optimal solution for the problem. This approach depends on finding efficient solutions for two problems. The first problem is minimizing total completi