This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some numerical examples are identified to show the utility and capability of the two proposed approaches. Mathematica®12 program has been relied upon in the calculations.
In the literature, several correlations have been proposed for hold-up prediction in rotating disk contactor. However,
these correlations fail to predict hold-up over wide range of conditions. Based on a databank of around 611
measurements collected from the open literature, a correlation for hold up was derived using Artificial Neiral Network
(ANN) modeling. The dispersed phase hold up was found to be a function of six parameters: N, vc , vd , Dr , c d m / m ,
s . Statistical analysis showed that the proposed correlation has an Average Absolute Relative Error (AARE) of 6.52%
and Standard Deviation (SD) 9.21%. A comparison with selected correlations in the literature showed that the
developed ANN correlation noticeably
In this work, Elzaki transform (ET) introduced by Tarig Elzaki is applied to solve linear Volterra fractional integro-differential equations (LVFIDE). The fractional derivative is considered in the Riemman-Liouville sense. The procedure is based on the application of (ET) to (LVFIDE) and using properties of (ET) and its inverse. Finally, some examples are solved to show that this is computationally efficient and accurate.
In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an
... Show MoreA biconical antenna has been developed for ultra-wideband sensing. A wide impedance bandwidth of around 115% at bandwidth 3.73-14 GHz is achieved which shows that the proposed antenna exhibits a fairly sensitive sensor for microwave medical imaging applications. The sensor and instrumentation is used together with an improved version of delay and sum image reconstruction algorithm on both fatty and glandular breast phantoms. The relatively new imaging set-up provides robust reconstruction of complex permittivity profiles especially in glandular phantoms, producing results that are well matched to the geometries and composition of the tissues. Respectively, the signal-to-clutter and the signal-to-mean ratios of the improved method are consis
... Show MoreCurrent search aims to identify the creative thinking of the kindergarten teachers and
solving professional problems among kindergarten teachers skills, and whether the level of
creative thinking in solving professional problems, according on marital status years of
service academic achievement of teachers as well as to identify the correlation between the
two variables the current sample consisted of (300) teachers to achieve the objectives of the
stndy , the researcher used two measures, one to measure creative thinking and the other to
measure the solution to the problems of professional kindergarten teachers skills. It has been
shown. validity and reliability of the two measures. The present stndy aims to identif
In this work, some of numerical methods for solving first order linear Volterra IntegroDifferential Equations are presented. The numerical solution of these equations is obtained by using Open Newton Cotes formula. The Open Newton Cotes formula is applied to find the optimum solution for this equation. The computer program is written in (MATLAB) language (version 6)
Abstract
Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t
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