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.
Malaysia's growing population and industrialisation have increased solid waste accumulation in landfills, leading to a rise in leachate production. Leachate, a highly contaminated liquid from landfills, poses environmental risks and affects water quality. Conventional leachate treatments are costly and time-consuming due to the need for additional chemicals. Therefore, the Electrocoagulation process could be used as an alternative method. Electrocoagulation is an electrochemical method of treating water by eliminating impurities by applying an electric current. In the present study, the optimisation of contaminant removal was investigated using Response Surface Methodology. Three parameters were considered for optimisation: the curr
... Show MoreTo evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and mult
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The environmental conditions are important factors, because they affect both the efficiency of a photovoltaic module and the energy load. This research was carried out experimentally and modeling was done in MATLAB –Simulink by monitoring the variation in power output of the system with environmental conditions such as solar radiation, ambient temperature, wind speed, and humidity of Baghdad city. From the results, the ambient temperatures are inversely proportional to humidity and the output power performance of the system, while the wind speed is directly proportional with the output power performance of the system.
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... Show MoreIn this work, studying the effect of ethylenediamine as a corrosion inhibitor was investigated for carbon steel in aerated HCl solution in range of 0.1-1N under dynamic conditions, i.e., rotational velocity of 400–1200 rpm in the temperature range 35 – 65 ºC. Weight loss method was employed in absence and presence of the inhibitor as an adsorption type in concentration range 1000 – 5000 ppm using rotating cylinder specimens. The experimental results showed that corrosion rate in absence and presence of inhibitor is increased with increasing temperature, rotational velocity and concentration of acid. It is decreased with increasing inhibitor concentration for the whole range of temperature, rotational velocity and concentrati
... Show MoreAutomatic speaker recognition may achieve remarkable performance in matched training and test conditions. Conversely, results drop significantly in incompatible noisy conditions. Furthermore, feature extraction significantly affects performance. Mel-frequency cepstral coefficients MFCCs are most commonly used in this field of study. The literature has reported that the conditions for training and testing are highly correlated. Taken together, these facts support strong recommendations for using MFCC features in similar environmental conditions (train/test) for speaker recognition. However, with noise and reverberation present, MFCC performance is not reliable. To address this, we propose a new feature 'entrocy' for accurate and robu
... Show MoreStatic and dynamic circumstances confirm that seepage is water movement through the earth dam’s embankment’s voids from upstream to downstream. Seepage is a quantity of fluid that has seeped through the permeable material or as the infiltration downward and lateral movement of water into soil or substrata from a source of supply such as a reservoir of a dam. In case of an earthquake strikes saturated soils, the water-filled pore spaces collapse, reducing the soil’s overall volume. The water pressure between individual soil grains is increased as a result of this action, and the grains can then move freely in the watery matrix. This reduces the soil’s resistance to shear str
This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.
Stress urinary incontinence (SUI) is involuntary urine leakage during activities that increase abdominal pressure such as coughing, sneezing and lifting of heavy weights. This is a very common disorder among women with history of multiple vaginal deliveries with an obstructed labor. SUI is considered one of the most distressing problems, especially for younger women, with severe quality of life implications, it caused by the loss of urethral support, usually as a consequence of the supporting structural muscles in the pelvis.
Objective: To prove and demonstrate the effect of a fractional CO2 micro-ablative laser (10600nm) in intra vaginal therapy for treating SUI and achieve a clinical improvement of t
... Show MoreIn this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.
Background: Acne is a common disorder experienced by adolescents and persists into adulthood in approximately 12%–14% of cases with psychological and social implications of high gravity. Fractional resurfacing employs a unique mechanism of action that repairs a fraction of skin at a time. The untreated healthy skin remains intact and actually aids the repair process, promoting rapid healing with only a day or two of downtime. Aims: This study, was designed to evaluate the safety and effectiveness of fractional photothermolysis (fractionated Er: YAG laser 2940nm) in treating atrophic acne scars. Methods: 7 females and 3 males with moderate to severe atrophic acne scarring were enrolled in this study that attained private clinic for Derm
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