This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical examples have been analyzed to demonstrate the efficacy of the new methods in comparison to the analytical method. Therefore, the numerical compression is carried out to confirm the efficiency and precision of the modified numerical methods. Significantly, the study demonstrates that the numerical outcomes of the proposed derived and modified numerical applied methods proved to be brilliant. Finally, based on the findings of the study, it could be said that the numerical outcomes of the test-problems using proposed and modified methods agree well with the analytical solutions. Hence, we can conclude that the proposed numerical methods that are derived or modified in the analytic study of this paper are quite efficient.
Rare earth metal oxides (REMOs) have gained considerable attention in recent years owing to their distinctive properties and potential applications in electronic devices and catalysts. Particularly, cerium dioxide (CeO2), also known as ceria, has emerged as an interesting material in a wide variety of industrial, technological, and medical applications. Ceria can be synthesized with various morphologies, including rods, cubes, wires, tubes, and spheres. This comprehensive review offers valuable perceptions into the crystal structure, fundamental properties, and reaction mechanisms that govern the well-established surface-assisted reactions over ceria. The activity, selectivity, and stability of ceria, either as a stand-alone catalyst or as
... Show MoreA critical milestone in nano-biotechnology is establishing reliable and ecological friendly methods for fabricating metal oxide NPs. Because of their great biodegradable, electrical, mechanical, and optical qualities, zirconia NPs (ZrO2NPs) attract much interest among all zirconia NPs (ZrO2NPs). Zirconium oxide (ZrO2) has piqued the interest of researchers throughout the world, particularly since the development of methods for the manufacture of nano-sized particles. An extensive study into the creation of nanoparticles utilizing various synthetic techniques and their potential uses has been stimulated by their high luminous efficiency, wide bandgap, and high exciton binding energy. Zirconium dioxide nano
... Show MoreIn this research, cyclic compounds derived from 2- furfural mercaptan (oxazole, triazoles) were synthesized, and their biological efficacy was measured and compared with standard drugs. Also, their effectiveness as anti-oxidant was measured and compared with ascorbic acid as a standard substance. Some of the synthesized compounds were deduced with good efficacy. © 2021 Sami Publishing Company. All rights reserved
In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.
The main intention of this study was to investigate the development of a new optimization technique based on the differential evolution (DE) algorithm, for the purpose of linear frequency modulation radar signal de-noising. As the standard DE algorithm is a fixed length optimizer, it is not suitable for solving signal de-noising problems that call for variability. A modified crossover scheme called rand-length crossover was designed to fit the proposed variable-length DE, and the new DE algorithm is referred to as the random variable-length crossover differential evolution (rvlx-DE) algorithm. The measurement results demonstrate a highly efficient capability for target detection in terms of frequency response and peak forming that was isola
... Show MoreTechnological advances have yielded new molecular biology-based methods for the diagnosis of infectious diseases. The newest and most powerful molecular diagnostic tests are available at regional and national reference laboratories, as well as at specialized centers that are certified to conduct metagenomic testing. Metagenomic assays utilize advances in DNA extraction technology, DNA sequence library construction, high throughput DNA sequencing and automated data analysis to identify millions of individual strands of DNA extracted from clinical samples. At present, metagenomic assays are only possible at a small number of special research, academic and commercial laboratories. Continued research in human and path
... Show MoreIn this paper we give definitions, properties and examples of the notion of type Ntopological space. Throughout this paper N is a finite positive number, N 2. The task of this paper is to study and investigate some properties of such spaces with the existence of a relation between this space and artificial Neural Networks (ïNN'S), that is we applied the definition of this space in computer field and specially in parallel processing
The term "nano gold," also known as "gold nanoparticles," is commonly used. These particles are extremely small, with a diameter of less than 100 nm, which is only a fraction of the width of a human hair. Due to their tiny size, nano gold particles are often found in a colloidal solution, where they are suspended in a liquid stabilizer. This colloidal gold is essentially another name for nano gold. The main method for producing gold nanoparticles in a colloidal solution is the citrate synthesis technique, which involves combining different solutions to precipitate the gold nanoparticles. In biological systems, copper complexes play a significant role at the active sites of many metalloproteins. These complexes have potential applications in
... Show MoreWithin this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an effic
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