In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

Dates are considered one of the most important foods consumed in Arab countries. Dates are commonly infested with the sawtoothed grain beetle, Oryzaephilus surinamensis. Consequently, the date yield, quantity, and quality (economic value and seed viability) are negatively affected. This study was designed to investigate the effectiveness of air evacuation as eco-friendly and safe control method against adult O. surinamensis. Insects were obtained from the infested date purchased from a private store in sakaka city, Aljouf region, Saudi Arabia. Air evacuation (using a vacuum pump) and food deprivation were applied to O. surinamensis, and insect mortality was observed daily in comparison with the control group (a

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

Background: Hypertension is a major global health concern that increases the risk of cardiovascular disease. Understanding the impact of age and treatment types on blood pressure control is essential for optimizing therapeutic strategies. Aim: This study aims to assess how different treatment types and patient age influence blood pressure control in hypertensive patients. Methodology: A binary logistic regression model was employed to analyze data from 48 patients diagnosed with hypertension. The study investigated the impact of two treatment regimens and patient age on the likelihood of achieving optimal blood pressure levels. The statistical significance of the findings was evaluated using chi-square tests and p-values. Results: T

The importance of specifying proper aggregate grading for achieving satisfactory performance in pavement applications has long been recognized. To improve the specifications for superior performance, there is a need to understand how differences in aggregate gradations within the acceptable limits may affect unbound aggregate base behavior. The effects of gradation on strength, modulus, and deformation characteristics of high-quality crushed rock base materials are described here. Two crushed rock types commonly used in constructing heavy-duty granular base layers in the State of Victoria, Australia, with three different gradations each were used in this study. The gradations used represent the lower, medium, and upper gradation li