This study aimed to extraction of essential oil from peppermint leaves by using hydro distillation methods. In the peppermint oil extraction with hydro distillation method is studied the effect of the extraction temperature to the yield of peppermint oil. Besides it also studied the kinetics during the extraction process. Then, 2^nd -order mechanism was adopted in the model of hydro distillation for estimation many parameters such as the initial extraction rate, capacity of extraction and the constant rat of extraction with various temperature. The same model was also used to estimate the activation energy. The results showed a spontaneous process, since the  Gibbs free energy had a value negative sign.

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

The DEM (Digital elevation model) means that the topography of the earth's surface (such as; Terrain relief and ocean floors), can be described mathematically by elevations as functions of three positions either in geographical coordinates, (Lat. Long. System) or in rectangular coordinates systems (X, Y, Z). Therefore, a DEM is an array number that represents spatial distributions of terrain characteristics. In this paper, the contour lines with different interval of high-resolution digital elevation model (1m) for AL-khamisah, The Qar Government was obtained. The altitudes ranging is between 1 m – 8.5 m, so characterized by varying heights within a small spatial region because it represents in multiple spots with flat surfaces.

A neutron induced deuteron emission spectra and double differential cross-sections (DDX), in 27Al (n, D) 26Mg, 51V (n, D)50Ti , 54Fe ( n, D)53Mn and 63Cu (n, D) 62Ni reactions, have been investigated using the phenomenological approach model of Kalbach. The pre-equilibrium stage of the compound nucleus formation is considered the main pivot in the discription of cross-section, while the equilibrium (pick up or knock out ) process is analyzed in the framework of the statistical theory of cluster reactions, Feshbach, Kerman, and Koonin (FKK) model. To constrain the applicable parameterization as much as possible and to assess the predictive power of these models, the calculated results have been compared with the experimental data and othe

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

            In this paper, several conditions are put in order to compose the sequence of partial sums ,  and  of the fractional operators of analytic univalent functions ,  and   of bounded turning which are bounded turning too.

  In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation.  The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation

The method of solving volterra integral equation by using numerical solution is a simple operation but to require many memory space to compute and save the operation. The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.

This paper presents a proposed method by using cascade-forward neural network to simulate volterra integral equations solutions. This method depends on training cascade-forward neural network by inputs which represent the mean of volterra integral equations solutions, the target of cascade-forward neural network is to get the desired output of this network. Cascade-forward neural

     In this article, we introduce a two-component generalization for a new generalization type of the short pulse equation was recently found by Hone and his collaborators. The coupled of nonlinear equations is analyzed from the viewpoint of Lie’s method of a continuous group of point transformations. Our results show the symmetries that the system of nonlinear equations can admit, as well as the admitting of the three-dimensional Lie algebra. Moreover, the Lie brackets for the independent vectors field are presented. Similarity reduction for the system is also discussed.