In this work, we are concerned with how to find an explicit approximate solution (AS) for the telegraph equation of space-fractional order (TESFO) using Sumudu transform method (STM). In this method, the space-fractional order derivatives are defined in the Caputo idea. The Sumudu method (SM) is established to be reliable and accurate. Three examples are discussed to check the applicability and the simplicity of this method. Finally, the Numerical results are tabulated and displayed graphically whenever possible to make comparisons between the AS and exact solution (ES).

This study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim

In this paper, the Reliability Analysis with utilizing a Monte Carlo simulation (MCS) process was conducted on the equation of the collapse potential predicted by ANN to study its reliability when utilized in a situation of soil that has uncertainty in its properties. The prediction equation utilized in this study was developed previously by the authors. The probabilities of failure were then plotted against a range of uncertainties expressed in terms of coefficient of variation. As a result of reliability analysis, it was found that the collapse potential equation showed a high degree of reliability in case of uncertainty in gypseous sandy soil properties within the specified coefficient of variation (COV) for each property. When t

    In this paper, the oscillatory and nonoscillatory qualities for every solution of fourth-order neutral delay equation are discussed. Some conditions are established to ensure that all solutions are either oscillatory or approach to zero as .  Two examples are provided to demonstrate the obtained findings.

In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)

in this paper fourth order kutta method has been used to find the numerical solution for different types of first liner

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.