This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica^®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving

Formation of Au–Ag–Cu ternary alloy nanoparticles (NPs) is of particular interest because this trimetallic system have miscible (Au–Ag and Au–Cu) and immiscible (Ag– Cu) system. So there is a possibility of phase segregation in this ternary system. At this challenge it was present attempts synthetic technique to generate such trimetallic alloy nanoparticles by exploding wire technique. The importance of preparing nanoparticles alloys in distilled water and in this technique makes the possibility of obtaining nanoparticles free of any additional chemical substance and makes it possible to be used in the treatment of cancer or diseases resulting from bacterial or virus with least toxic. In this work, three metals alloys Au-Ag-Cu

Wet granulation method was used instead of conventional pan coating  or fluidized –bed coating technique to prepare enteric-coated diclofenac sodium granules, using ethanolic solution of Eudragit^TM L100 as coating, binding and granulating agent .Addition of PEG400 or di-n-butyl phthalate as a plasticizer was found to improve the enteric property of the coat.

Part of the resulted granules was filled in hard gelatin capsules (size 0), while the other part was compressed into tablets with and without disintegrant.

The release profile of these two dosage forms in 0.1N HCl (pH 1.2)for 2 hours, and in phosphate buffer (pH 6.8) for 45 minutes as well as the release kinetic were compared with that of the en

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this paper, we will study and prove the existence and the uniqueness theorems
of solutions of the generalized linear integro-differential equations with unequal
fractional order of differentiation and integration by using Schauder fixed point
theorem. This type of fractional integro-differential equation may be considered as a
generalization to the other types of fractional integro-differential equations
Considered by other researchers, as well as, to the usual integro-differential
equations.

    In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.

This manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.

Metal oxide nanoparticles, including iron oxide, are highly considered as one of the most important species of nanomaterials in a varied range of applications due to their optical, magnetic, and electrical properties. Iron oxides are common compounds, extensive in nature, and easily synthesized in the laboratory. In this paper, iron oxide nanoparticles were prepared by co-precipitation of (Fe⁺²) and (Fe⁺³) ions, using iron (II and III) sulfate as precursor material and NH₄OH solution as solvent at 90°C. After the synthesis of iron oxide particles, it was characterized using X-ray diffraction (XRD), infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). These tests confirmed the obtaining o

The research was conducted to study the effect of adding different concentrations of AgNo3 Nanoparticles (0,0.5,1.0,1.5,2.0) mg/ l in the production of some secondary metabolic compounds(Quercetin, Luetolin and Apigenin) of plant Dodonaea viscosa L. Quantitative and qualitative analysis of secondary metabolites were estimated by using( HPLC ). The explants from leaves were culture on MS media supplemented with 2mg/l of 2,4-D, 0.5mg/l of NAA and 0.5 mg/l of BA for callus induction. Adding AgNo3 Nanoparticles (2 mg/l) cause in significant increase of Quercetin and Luetolin production, while adding AgNo3 Nanoparticles (0.5mg/l) led to significant increase of Apigenin in callus extract.

    Objective: The present study investigated the effects of different dose levels of Zinc oxide Nanoparticles (ZnO NPs) on the liver and kidney tissues in albino male mice. Methadology: ZnO NPs was administrated as a daily oral dose of (150, 350 mg/kg body weight) gavage for 2 weeks. Eighteen male mices were used by dividing them into three groups. Result: Histopathological examination of kidney and hepatic tissues treated with ZnO NPs showed toxicity changes compared with control group. Conclusion:This study demonstrated the ability of ZnO NPs to affect on kidney and liver tissues. Recommendation: More study needed to know the effect of different doses of nanoparticles on human health.