The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which transmit the memory and hereditary effects to other terms is examined. The theoretical results is applied to a numerical example. The calculated solution has a good agreement with the exact solution.
Abstract The research investigates in detail the fascinating story of its title character, which may work as an allegory for Africa itself in its past. Ama Ata Aidoo is miscellaneous writers who wrote in different literary genre like drama , short stories novel and , poetry and criticism . She is also an active feminist. Aidoo is against the colonial practice and its influence on African minds. Aidoo's play Anowa confronts painful issues in Africa's past, mostly those of the slave trade. She goes further to tackle issues of patriarchal domination and African feminism, like the relationships between individuals and society, women and motherhood, men and women, husbands and wives, mothers and daughters, and above all the future invasion
... Show MoreBackground/Aim: Capsicum annuum Grossum Senise, a widely cultivated sweet pepper in Iraq contains a diverse array of bioactive compounds such as polyphenols, carotenoids and capsinoids, known for their beneficial effects on health. The study aimed to employ advanced analytical techniques to elucidate the compound's chemical properties and concentration within this specific Capsicum cultivar, contributing to the growing body of knowledge regarding plant-derived sterols with potential nutraceutical application. Methods: This study focused on the extraction, isolation, purification and quantitative analysis of b-sitosterol from Iraqi Capsicum annuum Grossum. Advanced chromatographic and spectroscopic techniques were employed to ensure
... Show MoreThe paper presents the results of precise of the calculations of the diffusion of slow electrons in ionospheric gases, such as, (Argon – Hydrogen mixture, pure Nitrogen and Argon – Helium – Nitrogen) in the presence of a uniform electric field and temperature 300 Kelvin. Such calculations lead to the value Townsend's energy coefficient (KT) as a function of E/P (electric field strength/gas pressure), electric field (E), electric drift velocity (Vd), momentum transfer collision frequency ( ), energy exchange collision frequency ( ) and characteristic energy (D/?). The following physical quantities are deduced as function s E/P: mean free path of the electrons at unit pressure, mean energy lost by an electron per collision, mean velocit
... Show MoreFlurbiprofen (FLB) is chemically 2-(3- fluoro-4-phenyl phenyl) propanoic acid. It is a nonsteroidal anti-inflammatory drug (NSAID) used in the treatment of rheumatoid arthritis and osteoarthritis. Oral administration of this drug is associated with severe gastrointestinal side effects like ulceration and gastrointestinal bleeding. The solution to this problem lies in the fact that topically applied NSAIDs are safer than orally. This study aims to prepare different topical semisolid formulation of FLB as cream base (o/w), (w/o) and gel base using different gel-forming agents in different concentrations. Comparing characterization properties in addition to release and diffusion study for all the prepared formulas to select the best on
... Show MoreBackground: Conventional MR imaging is essential for diagnosis and evaluation of the posterior fossa tumors Objectives: To assess the value of diffusion weighted imaging and apparent diffusion coefficient in making distinction between different histological types of posterior fossa tumors.
Type of the study: Cross-sectional study.
Methods: Brain MRI and DWI assessed 19 patients (12 female and 7 male) with MRI diagnosis of posterior fossa tumors. absolute ADC values of contrast -enhancing solid tumor region and ADC ratio of solid tumor to ADC of normal -appearing deep White matter were compared with histological diagnosis postoperatively .The m
... Show MoreBackground: Prostatic adenocarcinoma is the most widely recognized malignancy in men and the second cause of cancer-related mortality encountered in male patients after lung cancer.
Aim of the study: To assess the diagnostic value of diffusion weighted imaging (DWI) and its quantitative measurement, apparent diffusion coefficient (ADC), in the identification and localization of prostatic cancer compared with T2 weighted image sequence (T2WI).
Type of the study: a prospective analytic study
Patients and methods: forty-one male patients with suspected prostatic cancer were examined by pelvic MRI at the MRI department of the Oncology Teaching Hospital/Medical City in Baghdad
... Show MoreIn this paper fractional Maxwell fluid equation has been solved. The solution is in the Mettag-Leffler form. For the corresponding solutions for ordinary Maxwell fluid are obtained as limiting case of general solutions. Finally, the effects of different parameters on the velocity and shear stress profile are analyzed through plotting the velocity and shear stress profile.

Gas hydrate formation poses a significant threat to the production, processing, and transportation of natural gas. Accurate predictions of gas hydrate equilibrium conditions are essential for designing the gas production systems at safe operating conditions and mitigating the problems caused by hydrates formation. A new hydrate correlation for predicting gas hydrate equilibrium conditions was obtained for different gas mixtures containing methane, nitrogen and carbon dioxide. The new correlation is proposed for a pressure range of 1.7-330 MPa, a temperature range of 273-320 K, and for gas mixtures with specific gravity range of 0.553 to 1. The nonlinear regression technique was applie
Abstract
Bivariate time series modeling and forecasting have become a promising field of applied studies in recent times. For this purpose, the Linear Autoregressive Moving Average with exogenous variable ARMAX model is the most widely used technique over the past few years in modeling and forecasting this type of data. The most important assumptions of this model are linearity and homogenous for random error variance of the appropriate model. In practice, these two assumptions are often violated, so the Generalized Autoregressive Conditional Heteroscedasticity (ARCH) and (GARCH) with exogenous varia
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