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.
The 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 MoreThis work aims to analyze a three-dimensional discrete-time biological system, a prey-predator model with a constant harvesting amount. The stage structure lies in the predator species. This analysis is done by finding all possible equilibria and investigating their stability. In order to get an optimal harvesting strategy, we suppose that harvesting is to be a non-constant rate. Finally, numerical simulations are given to confirm the outcome of mathematical analysis.
Abstract—The upper limb amputation exerts a significant burden on the amputee, limiting their ability to perform everyday activities, and degrading their quality of life. Amputee patients’ quality of life can be improved if they have natural control over their prosthetic hands. Among the biological signals, most commonly used to predict upper limb motor intentions, surface electromyography (sEMG), and axial acceleration sensor signals are essential components of shoulder-level upper limb prosthetic hand control systems. In this work, a pattern recognition system is proposed to create a plan for categorizing high-level upper limb prostheses in seven various types of shoulder girdle motions. Thus, combining seven feature groups, w
... Show MoreThis study examines the causes of time delays and cost overruns in a selection of thirty post-disaster reconstruction projects in Iraq. Although delay factors have been studied in many countries and contexts, little data exists from countries under the conditions characterizing Iraq during the last 10-15 years. A case study approach was used, with thirty construction projects of different types and sizes selected from the Baghdad region. Project data was gathered from a survey which was used to build statistical relationships between time and cost delay ratios and delay factors in post disaster projects. The most important delay factors identified were contractor failure, redesigning of designs/plans and change orders, security is
... Show MoreThe Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi
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