Abstract: The exact solution of a nonlinear fractional Volterra-Fredholm integro-differential equation is found in this paper through the successful application of the Abaoub Shkheam decomposition method. These techniques have a wider range of applications due to their dependability and decreased computational effort. 

ABSTRACT: This paper applies the Abaoub – Shkheam Decomposition Method (QDM) to obtaining solutions of linear fractional diffusion equations. The fractional derivative is described in the Caputo sense. Some illustrative examples are given, revealing the effectiveness and convenience of the method. 

Abstract: In this paper, a nonlinear fractional diffusion and wave equations are solved using the Abaoub-Shkheam Decomposition Method (QDM). The Caputo sense is used to characterise the fractional derivative. An example is provided to demonstrate the method's efficiency and practicality.

The purpose of this in-vitro study was to compare the fracture toughness of monolithic zirconia and multilayered zirconia, two commonly used materials in prosthodontic restorations. Fracture toughness is a key mechanical property that determines a material’s resistance to crack propagation under stress, which is crucial for the longevity and performance of dental restorations. A total of 20 zirconia discs (10 monolithic and 10 multilayered) were fabricated using Computer-Aided Design and Computer-Aided Manufacturing (CAD/CAM) technology. The discs were subjected to loading and fracture toughness was measured using the indentation method with a Vickers micro-hardness tester. The fracture toughness values for monolithic zirconia (Group 1) were significantly higher than those for multilayered zirconia (Group 2), with mean values of 5.394 ± 0.378 MPa·m1/2and 4.358 ± 0.394 MPa·m1/2, respectively (p < 0.0001). These findings suggest that monolithic zirconia offers superior mechanical performance, making it a more suitable material for high-stress applications, while multilayered zirconia may be preferred for anterior restorations, where esthetics are prioritized. The study highlights the trade-off between mechanical strength and esthetic appeal in the selection of zirconia materials for dental restorations and provides valuable insights for optimizing material choice in clinical prosthodontics.

This study is about conducting an economic comparison for establishing small and modular or large reactors in Libya, as analysts and decision makers often want to obtain estimates of the expected cost. There is a national project to establish the first nuclear station in Libya. The aim of this project is to study 19 infrastructure issues according to the International Atomic Energy Agency's Milestone Approach for any newcomer country that embarks on acquiring a nuclear station. One of these important elements of the study is the economic feasibility study of the project. For this, the IAEA INPRO NES simulator tool was used to make this comparison. During this study, the cost of a reactor unit with a capacity equal to 1085 megawatts was compared with approximately 4 equivalent units of the same capacity with small and modular reactors with a capacity of up to 300 megawatts -119921- per unit. These values were chosen to economically compare between a large reactor and four small units for the same total capacity of 1085 megawatts. From the results obtained, it was found that the estimated cost of 4 small and modular reactor units is $67.69 mill per kilowatt-hour, while the estimated cost of the LWR unit is $55.37 mill per kilowatt-hour, which means that establishing 4 SMRs units with a capacity of 300 megawatts per unit is more expensive than establishing a unit of a large 1085 MW reactor. A sensitivity analysis is applied for different discount rates, overnight construction costs, construction time to assess the levelized unit energy cost where the impact of the discount rate is obvious. There is a kind of trade-off between cost and the strength of the electrical network in Libya, as the electrical network is currently weak. It is possible to move forward with small and modular reactors or improve the electrical network to establish a nuclear station with large reactors.

This study highlights the simulation of a hypothetical fracture in the largest beam tube connected to the core of the Tajoura Nuclear Research Centre's (TNRC) reactor with low enrichment uranium, which produces a maximum thermal power equal to 9.7MW. This study was conducted for the purpose of evaluating the safety of the reactor core when the fracture occurs. The reactor core is cooled in normal operation by downward pumping of coolant (light water) and forced convection, while the reactor core is cooled by natural convection when the cooling pumps stop and after the emergency tank is filled to extract the decay heat. As a result of the temperature difference between the water in the reactor core and the reactor pool, and as a result of the density difference, a reverse flow of coolant occurs in the upward direction. When a break occurs in one of the beam tubes, the Loss of Coolant Accident (LOCA) is started. Consequently, the water level will decrease, and when it reaches 7.4 meters, the cooling pumps will coast down, and thus the SCRAM takes place at the reactor. Because the beam tubes are located in the middle of the reactor core, the water level in the reactor pool will continue to decrease until the denudation of the core takes place when the reactor core is denudated and exposed to air. In this case, the reactor is cooled by two means of heat transfer: natural convection and radiation. Radiation takes place at high temperature differences, in this case, most of heat transfer occurs by natural convection. The MATLAB program was used in this study to perform hydraulic calculations over time in the hottest cell in the reactor core. The results showed that the surface temperatures of the clad exceed the maximum temperature allowed for the surface of the clad (102°C). The temperatures obtained in the surface clad (Aluminum) were compared with the melting temperature, which is 660°C, and it was found that at time 260 sec the clad surface temperature exceeds the melting point. Therefore, it was noticed that when the reactor core is exposed to the air, there is no ability to remove the decay heat by natural convection nor radiation. Thus, temperatures will rise, which will lead to fuel deterioration. To avoid this, it is better to operate the reactor at lower powers thus the decay heat becomes less. In addition, closing the shutters of the beam tubes when the breakage occurs to reduce the amount of leakage and loss of the coolant.

This study aimed to evaluate and compare the microhardness of monolithic zirconia and multilayered zirconia to investigate the influence of material composition and structural design on their mechanical properties. Cylindrical specimens were designed using AutoCAD software and fabricated from monolithic zirconia (Group A) and multilayered zirconia (Group B blocks via CAD/CAM milling systems. The specimens were sectioned into discs with a diameter of 10 mm and a thickness of 1.5 mm. Microhardness testing was performed on these discs using a standardized protocol. Statistical analysis was conducted using a student’s t-test (P < 0.05) with a sample size of 10 specimens per group to ensure 80% power and 95% confidence. Results revealed significant differences in microhardness between monolithic and multilayered zirconia. Monolithic zirconia exhibited superior hardness, attributable to its single-layered structure, which enhances its mechanical strength and wear resistance. In contrast, multilayered zirconia, while exhibiting lower microhardness, demonstrated esthetic advantages due to its gradient layering and maintained sufficient durability for clinical use. The findings underscore the impact of zirconia composition and structural design on mechanical properties, providing clinicians with valuable insights for material selection. While monolithic zirconia is ideal for high-load posterior restorations, multilayered zirconia offers an esthetic solution with adequate mechanical performance, making it suitable for anterior applications.