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 research documents the initial finding of Chloris pycnothrix Trin., frequently referred to as spiderweb chloris, in Libya, particularly from the Ariggiba region close to Sabha city. This grass, originating from tropical and subtropical regions, is versatile and may become invasive. It was recognized via morphological examination during field surveys in 2023–2024, with samples stored in a herbarium. The species flourishes in alluvial plains as well as in disturbed habitats like road shoulders. It can be mistaken for Chloris virgata, although they differ in some important morphological aspects. It was previously believed that only one species of Chloris existed in Libya. This study provides a revision and an identification key for them in the context of Libyan flora. The tolerant nature of C. pycnothrix to drought, combined with its ability to colonize poorly maintained land, makes its potential introduction—most likely through anthropogenic means—alarming ecologically and emphasizes the need for management strategies to contain its spread and monitor its impact.