The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

Bipedal robots, designed to replicate human locomotion, face significant balance challenges due to instability and high degrees of freedom. This study examines dynamical models, balance control strategies, and locomotion methodologies. Dynamical models are categorized into simplified, centroidal dynamics, and whole-body dynamics models. Simplified models, such as the Linear Inverted Pendulum Model (LIPM), approximate the robot as a point mass at the Center of Mass (CoM) but neglect upper-body dynamics and complex terrain interactions. Centroidal dynamics models incorporate CoM motion, contact forces, and angular momentum for improved disturbance rejection but require extensive computational resources. Whole-body models achieve high

This paper presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt  properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1)  is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method  (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to

Determination and evaluation of principal minerals in Negella sativa by atomic absorption technical methods were showed, using wet ashing method. This work was done on Negella sativa because of wide using of this plant in many formulations ( in food or medicine ).two types of atomic absorptions were used : first, flame atomic absorption spectroscopy, for minerals of high concentrations such as, Na, Mg, K, Fe, Ca, Li, Ni, Zn, Mn, Cu. Second, flameless atomic absorption spectroscopy, for minerals of low concentrations such as, Al, Si, V, B, Pb, Co, Cd, Cr ,Si, Hg, Sn .The results showed the existence of many minerals in Negella sativa useful to human sanity with acceptable dietary allowance. On other side, the presence of harmful m

In this study, the Earth's surface was studied in Razzaza Lake for 25 years, using remote sensing methods. Images of the satellites Landsat 5 (TM) and 8 (OLI) were used to study and determine the components of the land cover. The study covered the years 1995-2021 with an interval of 5 years, as this region is uninhabited, so the change in the land cover is slow. The land cover was divided into three main classes and seven subclasses and classified using the maximum likelihood classifier with the help of training sets collected to represent the classes that made up the land cover. The changes detected in the land cover were studied by considering 1995 as a reference year. It was found that there was a significant reduction in the water mass

An experimental study was performed to estimate the forced convection heat transfer performance and the pressure drop of a single layer graphene (GNPs) based DI-water nanofluid in a circular tube under a laminar flow and a uniform heat flux boundary conditions. The viscosity and thermal conductivity of nanofluid at weight concentrations of (0.1 to 1 wt%) were measured. The effects of the velocity of flow, heat flux and nanoparticle weight concentrations on the  enhancement of the heat transfer are examined. The Nusselt number of the GNPs nanofluid was enhanced as the heat flux and the velocity of flow rate  increased, and the maximum Nusselt number  ratio (Nu nanofluid/ Nu base fluid)   and thermal performance factor

The problem of Multicollinearity is one of the most common problems, which deal to a large extent with the internal correlation between explanatory variables. This problem is especially Appear in economics and applied research, The problem of Multicollinearity has a negative effect on the regression model, such as oversized variance degree and estimation of parameters that are unstable when we use the Least Square Method ( OLS), Therefore, other methods were used to estimate the parameters of the negative binomial model, including the estimated Ridge Regression Method and the Liu type estimator, The negative binomial regression model is a nonline

In the analysis of multiple linear regression, the problem of multicollinearity and auto-correlation drew the attention of many researchers, and given the appearance of these two problems together and their bad effect on the estimation, some of the researchers found new methods to address these two problems together at the same time. In this research a comparison for the performance of the Principal Components Two Parameter estimator (PCTP) and The (r-k) class estimator and the r-(k,d) class estimator by conducting a simulation study and through the results and under the mean square error (MSE) criterion to find the best way to address the two problems together. The results showed that the r-(k,d) class estimator is the best esti