In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall

This study examines the structural performance of concrete-encased pultruded Glass Fiber Reinforced Polymer (GFRP) I-sections with shear connections. It specifically focuses on how different parameters affect the latter’s ductility, flexural strength, and load-carrying capacity. The key variables studied include various shear connector types, spacing, and geometries, as well as the compressive strength of concrete and the properties of GFRP. The finite element modeling and experimental validation show that the shear connectors significantly improve the ductility, ultimate capacity, and load transmission efficiency. The present review emphasizes that the shear connectors greatly enhance the structural performance when they are prop

This study investigates the implementation of Taguchi design in the estimation of minimum corrosion rate of mild-steel in cooling tower that uses saline solution of different concentration. The experiments were set on the basis of Taguchi’s L16 orthogonal array. The runs were carried out under different condition such as inlet concentration of saline solution, temperature, and flowrate. The Signal-to- Noise ratio and ANOVA analysis were used to define the impact of cooling tower working conditions on the corrosion rate. A regression had been modelled and optimized to identify the optimum level for the working parameters that had been founded to be 13%NaCl, 35ᴼC, and 1 l/min. Also a confirmation run to establish the p

This research aimed to predict the permanent deformation (rutting) in conventional and rubberized asphalt mixes under repeated load conditions using the Finite Element Method (FEM). A three-dimensional (3D) model was developed to simulate the Wheel Track Testing (WTT) loading. The study was conducted using the Abaqus/Standard finite element software. The pavement slab was simulated using a nonlinear creep (time-hardening) model at 40°C. The responses of the viscoplastic model under the influence of the trapezoidal amplitude of moving wheel loadings were determined for different speeds and numbers of cycles. The results indicated that a wheel speed increase from 0.5Km/h to 1.0Km/h decreased the rut depth by about 22% and 24% in conv

Vibration is a source of energy that can be beneficial or harmful based on the application. Vibration can affect the function of any structure; however, Ceramic matrix composite (CMC) is one of these structures. Whereby less studies have been concentrated on study its function specially when electromagnetic wave (microwave) exposed on its surface to perform its designed function. To address this concept, SiC composite has been fabricated which is designed to have a transparent characteristics to microwave. External vibration had been applied on its surface to monitor how much influence could nanoscale amplitude vibration damage the microwave interaction. The source of vibration was applied from piezoelectric and the vibration was monitored

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

New series of metal ions complexes have been prepared from the new ligand [4-Amino-N-(5-methyl-isaxazol-3-yl)-benzenesulfonamide] derived from Sulfamethoxazole and 3-aminophenol. Accordingly, mono-nuclear Mn(II), Fe(III), Co (II), and Rh(III) complexes were prepared by the reaction of previous ligand with MnCl₂.4H₂O, CoCl₂.6H₂O, FeCl₃.6H₂O and RhCl₃H₂O, respectively. The compounds have been characterized by Fourier-transform infrared (FTIR), ultraviolet–visible (UV–vis), mass,  ¹H-, and ¹³C-nuclear magnetic resonance (NMR) spectra and thermo gravimetric analysis (TGA& DSC) curve, Bohr magnetic (B.M.), elemental microanal