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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).

Abstract 

The catalytic cracking conversion of Iraqi vacuum gas oil was studied on large and medium pore size (HY, HX, ZSM-22 and ZSM-11) of zeolite catalysts. These catalysts were prepared locally and used in the present work. The catalytic conversion performed on a continuous fixed-bed laboratory reaction unit. Experiments were performed in the temperature range of 673 to 823K, pressure range of 3 to 15bar, and LHSV range of 0.5-3h^-1. The results show that the catalytic conversion of vacuum gas oil increases with increase in reaction temperature and decreases with increase in LHSV. The catalytic activity for the proposed catalysts arranged in the following order:

HY>H

يعد التقطيع الصوري من الاهداف الرئيسة والضرورية في المعالجات الصورية للصور الرقمية، فهو يسعى الى تجزئة الصور المدروسة الى مناطق متعددة اكثر نفعاً تلخص فيها المناطق ذات الافادة لصور الاقمار الصناعية، وهي صور متعددة الاطياف ومجهزة من الاقمار الصناعية باستخدام مبدأ الاستشعار عن بعد والذي اصبح من المفاهيم المهمة التي تُعتمد تطبيقاته في اغلب ضروريات الحياة اليومية، وخاصة بعد التطورات المتسارعة التي شهد

Beta-irradiation effects on the microstructure of LDPE samples have been investigated
using Positron Annihilation Lifetime Technique (PALT). These effects on the orthopositronium
(o-Ps) Lifetime t3, the free positron annihilation lifetime 2 t , the free-volume
hole size (Vh) and the free volume fraction (fh) were measured as functions of Beta
irradiation - dose up to a total dose of 30.28 kGy.
The results show that the values of t3, Vh and fh increase gradually with increasing Beta
dose up to a total dose of 1.289 kGy, and reach a maximum increment of 17.4%, 32.8% and
5.86%, respectively, while t2 reachs maximum increment of 211.9% at a total dose of 1.59
kGy. Above these doses, the values show nonlinear changes u

Background: Severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) is still a severe threaft for human health currently, and the researches about it is a focus topic worldwide.

Aim of the study: In this study, we will collect some laboratory results of the patients with coronavirus disease (COVID-19) to assess the function of liver, heart, kidney and even pancreas. 

Subjects and Methods: Laboratory results of the patients with COVID-19 are collected. The biochemical indices are classified and used to assess the according function of liver, heart, kidney; meantime, and blood glucose is also observed and taken as an index to roughly evaluate pancreas.

Results: There were some in

This paper is concerned with introducing and studying the new approximation operators based on a finite family of d. g. 'swhich are the core concept in this paper. In addition, we study generalization of some Pawlak's concepts and we offer generalize the definition of accuracy measure of approximations by using a finite family of d. g. 's.

Sewer network is one of the important utilities in modern cities which discharge the sewage from all facilities. The increase of population numbers consequently leads to the increase in water consumption; hence waste water generation. Sewer networks work is very expensive and need to be designed accurately. Thus construction effective sewer network system with minimum cost is very necessary to handle waste water generation.

 In this study trunk mains networks design was applied which connect the pump stations together by underground pipes for too long distances. They usually have large diameters with varying depths which consequently need excavations and gathering from pump stations and transport the sewage