This paper aims to find new analytical closed-forms to the solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability
The global oil market is one of the most important markets in the world and occupies especially for countries consuming and producing countries, and the status of understanding of the mechanism for determining prices in the market help to stand on many factors affecting oil demand and supply of oil and geopolitical factors, climate and alternative sources of energy .. etc. factors, and that the main objective of the research is to study the causes and results left behind by the oil price shocks in the world market, and the movement of these factors be through a cycle of energy that explain the strength of competition between these factors and their effects on prices, when demand increases evolution Large image leads to significan
... Show MoreThe aim of this article is to study the dynamical behavior of an eco-epidemiological model. A prey-predator model comprising infectious disease in prey species and stage structure in predator species is suggested and studied. Presumed that the prey species growing logistically in the absence of predator and the ferocity process happened by Lotka-Volterra functional response. The existence, uniqueness, and boundedness of the solution of the model are investigated. The stability constraints of all equilibrium points are determined. The constraints of persistence of the model are established. The local bifurcation near every equilibrium point is analyzed. The global dynamics of the model are investigated numerically and confronted with the obt
... Show MoreThe present research had dealt with preparing bars with the length of about (13 cm) and adiametar of (1.5 cm) of composite materials with metal matrix represented by (Al-Cu-Mg) alloy cast enforced by (ZrO2) particles with chosen weight percentages (1.5, 2.5 ,3.5, 5.5 %). The base cast and the composite materials were prepared by casting method by uses vortex Technique inorder to fix up (ZrO2) particles in homogeneous way on the base cast. In addition to that, two main groups of composite materials were prepared depending on the particles size of (ZrO2) , respectively. &n
... Show MoreThe necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
... Show MoreThis 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 nonli
... Show MoreThe organation ⁄monomer N-naphthylacrylamide (NAA) was prepared; subsequently the synthesized monomer was successfully copolymerized with acrylicacid (AA) and methylacrylate (MA) by free radical technique using dry benzene as solvent and benzoyl peroxide (BPO) as initiator. The overall conversion was kept low (≤ 10% wt/wt) for all studies copolymers samples. The synthesized monomer and copolymers were characterized using Fourier transform infrared spectroscopy (FT-IR), and their thermal properties were studied by DSC and TGA. The copolymers compositions were determined by elemental analysis. Kelen-Tudes and Finmman-Ross graphical procedures were employed to determine the monomers reactivity ratios. The der
... Show MoreThe organation ⁄monomer N-naphthylacrylamide (NAA) was prepared; subsequently the synthesized monomer was successfully copolymerized with acrylicacid (AA) and methylacrylate (MA) by free radical technique using dry benzene as solvent and benzoyl peroxide (BPO) as initiator. The overall conversion was kept low (≤ 10% wt/wt) for all studies copolymers samples. The synthesized monomer and copolymers were characterized using Fourier transform infrared spectroscopy (FT-IR), and their thermal properties were studied by DSC and TGA. The copolymers compositions were determined by elemental analysis. Kelen-Tudes and Finmman-Ross graphical procedures were employed to determine
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