This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

The increasing availability of computing power in the past two decades has been use to develop new techniques for optimizing solution of estimation problem. Today's computational capacity and the widespread availability of computers have enabled development of new generation of intelligent computing techniques, such as our interest algorithm, this paper presents one of new class of stochastic search algorithm (known as Canonical Genetic' Algorithm ‘CGA’) for optimizing the maximum likelihood function strategy is composed of three main steps: recombination, mutation, and selection. The experimental design is based on simulating the CGA with different values of are compared with those of moment method. Based on MSE value obtained from bot

This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can hav

The reaction of LAs-Cl8 : [ (2,2- (1-(3,4-bis(carboxylicdichloromethoxy)-5-oxo-2,5- dihydrofuran-2-yl)ethane – 1,2-diyl)bis(2,2-dichloroacetic acid)]with sodium azide in ethanol with drops of distilled water has been investigated . The new product L-AZ :(3Z ,5Z,8Z)-2- azido-8-[azido(3Z,5Z)-2-azido-2,6-bis(azidocarbonyl)-8,9-dihydro-2H-1,7-dioxa-3,4,5- triazonine-9-yl]methyl]-9-[(1-azido-1-hydroxy)methyl]-2H-1,7-dioxa-3,4,5-triazonine – 2,6 – dicarbonylazide was isolated and characterized by elemental analysis (C.H.N) , 1H-NMR , Mass spectrum and Fourier transform infrared spectrophotometer (FT-IR) . The reaction of the L-AZ withM+n: [ ( VO(II) , Cr(III) ,Mn(II) , Co(II) , Ni(II) , Cu(II) , Zn(II) , Cd(II) and Hg(II)] has been i

The modification of hydrophobic rock surfaces to the water-wet state via nanofluid treatment has shown promise in enhancing their geological storage capabilities and the efficiency of carbon dioxide (CO2) and hydrogen (H2) containment. Despite this, the specific influence of silica (SiO2) nanoparticles on the interactions between H2, brine, and rock within basaltic formations remains underexplored. The present study focuses on the effect of SiO2 nanoparticles on the wettability of Saudi Arabian basalt (SAB) under downhole conditions (323 K and pressures ranging from 1 to 20 MPa) by using the tilted plate technique to measure the contact angles between H2/brine and the rock surfaces. The findings reveal that the SAB's hydrophobicity intensif