The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.
In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.
in this paper the second order neutral differential equations are incestigated are were we give some new suffucient conditions for all nonoscillatory
In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.
Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.
Reverse Phase High Performance Liquid Chromatography (RP-HPLC) was coupled with ultraviolet absorption sepectoscopy (UV) for separation and identification of Naphthalene, Acenaphthylene, Pyrene, Benz{a} anthracene and 1,3,2,4-Dibenzanthracene. RP-HPLC was performed on an ODS-C18 column (150×4.6 mm I.D) using acetonitrile–buffer phosphate as mobile phase. UV absorption spectra of the elutes was detected in 254 nm, and studying the chromatographic variables include organic modifier ratio, PH, column temperature and concentration of buffer to maximize resolution and minimize separation time. the results showed that using mobile phase( 80:20) v/v acetonitrile:0.01M phosphate buffer solution at PH 6 with flow rate 1ml/min and column te
... Show MoreNaturally occurring radioactive materials (NORM) contaminated sites at Al-Rumaila Iraqi oil fields have been characterized as a part of soil remediation project. Activity of radium isotopes in contaminated soil have been determined using gamma spectrometer High Purity Germanium detector (HPGe) and found to be very high for Al-Markezia, Al-Qurainat degassing stations and storage area at Khadhir Almay region. The activity concentration of samples ranges from 6474.11±563.8 Bq/kg to 1232.5±60.9 Bq/kg with mean value of 3853.3 Bq/kg for 226Ra, 843.59±8.39 Bq/kg to 302.2±9.2 Bq/kg with mean value of 572.9 Bq/kg for 232Th and 294.31±18.56 Bq/kg to 156.64±18.1 Bq/kg with mean value of 225.5 for 40K. S
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