In this paper, we introduce and discuss an algorithm for the numerical solution of some kinds of fractional integral and fractional integrodifferential equations. The algorithm for the numerical solution of these equations is based on iterative approach. The stability and convergence of the fractional order numerical method are described. Finally, some numerical examples are provided to show that the numerical method for solving the fractional integral and fractional integrodifferential equations is an effective solution method.
The taxonomy of Ficus L., 1753 species is confusing because of the intense morphological variability and the ambiguity of the taxa. This study handled 36 macro-morphological characteristics to clarify the taxonomic identity of the taxa. The study revealed that Ficus is represented in the Egyptian gardens with forty-one taxa; 33 species, 4 subspecies and 4 varieties, and classified into five subgenera: Ficus Corner, 1960; Terega Raf., 1838; Sycomorus Raf., 1838; Synoecia (Miq.) Miq., 1867, and Spherosuke Raf.,1838; out of them seven were misidentified. Amongst, four new Ficus taxa were recently introduced to Egypt namely: F. lingua subsp. lingua Warb. ex De Wild. & T. Durand, 1901; F. pumila L., 1753; F. rumphii Blume, 1825, and F. su
... Show MoreThis paper deals with numerical approximations of a one-dimensional semilinear parabolic equation with a gradient term. Firstly, we derive the semidiscrete problem of the considered problem and discuss its convergence and blow-up properties. Secondly, we propose both Euler explicit and implicit finite differences methods with a non-fixed time-stepping procedure to estimate the numerical blow-up time of the considered problem. Finally, two numerical experiments are given to illustrate the efficiency, accuracy, and numerical order of convergence of the proposed schemes.
A numerical study of the double-diffusive laminar natural convection in a right triangular solar collector has been investigated in present work. The base (absorber) and glass cover of the collector are isothermal and isoconcentration surfaces, while the vertical wall is considered adiabatic and impermeable. Both aiding and opposing buoyancy forces have been studied. Governing equations in vorticity-stream function form are discretized via finite-difference method and are solved numerically by iterative successive under relaxation (SUR) technique. Computer code for MATLAB software has been developed and written to solve mathematical model. Results in the form of streamlines, isotherms, isoconcentration, average Nusselt, and average Sherw
... Show MoreThe discharge of dyes into the water is a significant source of pollution, which is especially concerning given that textile mills are the primary contributor. Nanomaterial-based solutions to this issue have required extensive research and investigation due to their complex nature. In this research, novel nanoparticle were successfully synthesized using the leaves of the Eruca sativa plant. The nano was analyzed using scanning and transmission electron microscopy (SEM and TEM) measurements, and their crystal structure was determined using the X-ray diffraction technique (XRD). The incorporation of NPs resulted in an increase in the uptake of the Cibacron red dye. At a contact time of 30 minutes, observed a faster adsor
... Show MoreWriting in English is one of the essential factors for successful EFL learning .Iraqi students at the preparatory schools encounter problems when using their background knowledge in handling subskills of writing(Burhan,2013:164).Therefore, this study aims to investigate the 4thyear preparatory school students’ problems in English composition writing, and find solutions to these pro
... Show MoreIn this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov
... Show MoreThis work investigates the effect of earthquakes on the stability of a collective pile subjected to seismic loads in the soil layer. Plaxis 3D 2020 finite element software modeled pile behavior in dry soils with sloping layers. The results showed a remarkable fluctuation between the earthquakes, where the three earthquakes (Halabja, El Centro, and Kobe) and the acceleration peak in the Kobe earthquake had a time of about 11 seconds. Different settlement results were shown, as different values were recorded for the three types of earthquakes. Settlement ratios were increased by increasing the seismic intensity; hence the maximum settlement was observed with the model under the effect of the Kobe earthquake (0.58 g), where
... Show MoreSloped solar chimney system is a solar chimney power plant with a sloped collector. Practically, the sloped collector can function as a chimney, then the chimney height can be reduced and the construction cost would be reduced.The continuity, Naver-stockes, energy and radiation transfer equations have been solved and carried out by Fluent software. The governing equations are solved for incompressible, 3-D, steady, turbulent standard model with Boussiuesq approximation to develop for the sloped solar chimney system in this study and evaluate the performance of solar chimney power plant in Baghdad city of Iraq numerically by Fluent (14) software with orking conditions such as solar radiation intensity (30
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