In Saxon granulite mountains, significant deposits of hydrosiliceous nickel are characterized by their

relevant metal content, average metal concentrations, and thickness. The hydrosilicate deposits are Nirich

residue, formed by serpentinization process, due to the replacement process of nickel in the

immediate vicinity of serpentinites and nickel-bearing ore minerals (e.g., talc, chlorite nontronite,

cordierite, nepouite, other oxides and hydroxide magnesium minerals). X-ray and chemical analysis

indicate that the study area consists mainly of nickel, magnesium silicates, and hydrosilicate minerals,

with concentration of Ni varying from 2% to a few tens of ppm. A variety of lithological compositions

are present in these deposits, which are influenced by ultramafic rocks (serpentinite), talc and chloritic

clays, etc. The analysis of the mineralogical and geochemical composition of the Ni-ores also evidences

that the sources of Ni are ultramafic rocks derived from the mantle and concentration by

serpentinitization processes under discrete tectonic and metallogenic events. An important consideration

in the economics of these deposits is the mode of occurrence of nickel ores.

In this study, we numerically investigate two significant medical models, Ebola Viral Disease (EVD) and Blood Ethanol Concentration (BEC) models-both formulated using Caputo-fractional derivatives. We develop and apply the Modified Fractional Euler Method (MFEM) for their solution, with a specific focus on error analysis. Comparative studies with the classical Runge-Kutta fourth-order method (RK4M) demonstrate that MFEM provides a computationally efficient and accurate alternative for solving such systems. The major features of the given procedure are its ease of application to this type of problem and other systems in various fields, in addition to the absence of numerical errors accumulating. Finally, we can control the increase in the convergence rate and the stability of the simulation process. The convergence examination and error estimation for the suggested scheme are also included. The importance of this study also lies in its contribution to our understanding of the dynamics of these two models in their fractional form. In addition, those numerical investigations demonstrate how control parameters affect specific components within these models.

Abstract:

The Jabal Fezzan's xenolith has been intruded during Pan-African metamorphism, characterized by (high pressure and medium temperature), this process results in the formation of the biotite, muscovite, and kyanite metamorphic zones. There is a slight increase in the degree of metamorphism as it reaches the biotite zone. It consists of foliated, medium- to coarse-grained schists, mostly biotite, muscovite, and kyanite, additionally plagioclase and quartz, as well as zircon, rutile, and Fe oxides. The microscopical evidence indicates that iron-rich biotite in pelitic schists undergoes a series of chemical reactions that cause it to be formed and transformed into other minerals. P-T diagrams suggest that rocks in the study area might have been formed during collisions and decompressions of thickened continental crust. They are derived from sedimentary rocks such as greywacke, which contain high levels of Si4+ and Al3+. As P-T conditions pass through, the biotite isograd and biotite forms. This study highlighted the oldest metamorphic rocks in southern Libya, enhancing the understanding of the mantle source protolith metasomatism, and reducing the information gap between petrochemical significance and the evolutionary stage of Pan-African metamorphism in southern Libya through study xenolith outcrops in more detail.

In Mobile Ad Hoc Network (MANET) the applications of a multimedia system like video, audio broadcasting needs the path at which the data transmit might be reliable, delay-sensitive, and energy-efficient one. In addition, the delivery of information in vehicular networks (VANETs) is regarded as a demanding one because of high mobility and invariable topological difference. An existing routing protocol of ad hoc network fail to function better in terms of QoS metrics like packet delivery ratio (PDR), delay and so on., where there are heavy traffic and high mobility. So as to overcome the existing drawbacks, the proposed technique is implemented. In the proposed mechanism, the system model is initialized, and the route discovery process is carried by sending a route request. The multipath decision making (MPDM) scheme is employed to ensure the best route availability and the probability of link failure. Once the multipath decision-making condition is satisfied, the route path is established, and the communication takes place based on QoS constraint. Fuzzy based link monitoring scheme is employed to check the probability of link failure. Finally, the performance analysis is carried, and the comparison is made for proposed and existing mechanisms to prove the efficiency of the proposed scheme.

 We give the approximate solution of the Riccati/Logistic differential equations (RDE/LDE). The suggested approach depends on the homotopy perturbation method developed with the Chebyshev series (CHPM). A study of the convergence analysis of CHPM is presented. The residual error function is calculated and used as a basic criterion in evaluating the accuracy and efficiency of the given numerical technique. We use the exact solution and the Runge-Kutta method of fourth order for comparison with the results of the method used. Through these results, we can confirm that the applied method is an easy and effective tool for the numerical simulation of such models. Illustrative models are given to confirm the validity and usefulness of the proposed procedure. 

In this research, we investigated the Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral constraints. We presented novel sufficient conditions for the uniqueness of the solution. Moreover, we analyzed the continuous dependence of the solution on some functions and parameters. Additionally, we proved the Hyers-Ulam stability of the problem. To demonstrate the applicability of our results, we included several examples. The present study was located in the space L1[0, T]. The techniques of Schauder’s fixed point theorem and Kolmogorov’s compactness criterion were the primary tools utilized in this work. These contributions offer a comprehensive framework for understanding the qualitative behavior of the fractional-order pantograph equation.