Results in Nonlinear Analysis

On certain fixed point theorems for F-contractions in 2-metric spaces and their application

2024-11-22T11:11:31+03:00

This paper focuses on investigating F-contractions in 2-metric spaces and proving multiple fixed point theorems related to these contractions. Through the definition and analysis of F-contraction map-pings in the context of 2-metric spaces, the research sheds light on the existence and uniqueness of fixed points. The findings enhance the over-all comprehension of fixed point theory and its applications, providing useful resources for further exploration in mathematical analysis and associated areas.

Blow-up solutions of a system of nonlinear the Klein-Gordon-Fock Type wave equations

2024-11-15T10:49:53+03:00

We consider the initial boundary value problem for a system of strongly damped wave equations with homogeneous Dirichlet boundary conditions and a nonlinear source term. By applying a modification of the concavity method, we demonstrate that the solutions blow up for $p<3$ with arbitrary positive initial data. Furthermore, we show that the global solvability of the problem for
$p\geq 3$.

Generalized cayley graphs and group structure: Insights from the direct products of P₂ and C₃

2024-12-30T15:12:16+03:00

This work introduces a generalization of Cayley graphs, denoted Caym(ψ, S), where ψ is a finite group and S is a non-empty subset of ψ. In this construction, vertices are represented by m-dimensional column vectors with entries in ψ, and adjacency is determined by a matrix-based condition involving the inverse elements and a matrix of elements from S. We focus on elucidating the structure and fundamental properties of Caym(ψ, S) when the classical Cayley graph Cay(ψ, S) corresponds to the direct products P2 × P2
and P2 × C2. Through rigorous analysis, we reveal distinct structural characteristics arising from these specific group structures and their associated generating sets. The generalized Cayley graph, denoted as Caym(ψ, S), is a graph where the vertex set consists of all column matrices Xm, with each matrix having elements from the set Ψ. Two vertices Xm and Ym are adjacent if and only if Ym
−1, the inverse of Ym, is a column matrix where each entry corresponds to the inverse of the associated element in Ψ. Our findings provide valuable insights into the interplay between algebraic properties of groups and the topological features of their generalized Cayley graph representations. This study contributes to a deeper understanding of generalized Cayley graphs and their potential
applications in diverse fields such as network theory, coding theory, and cryptography.

Derivation of Sawada-Kotera and Kaup-Kupershmidt equations KdV Flow Equations from Derivative Nonlinear Schrödinger Equation (DNLS)

2024-12-05T12:59:43+03:00

The mathematical models of problems that arise in almost every branch of science are nonlinear equations of evolution (NLEE). In the past years, equations of formation have gained a significant place in applied mathematics. This study is about the multiple scales method, known as the perturbation method, for the derivative nonlinear Schrödinger (DNLS) equation. In this report, the multiple scales method was applied for the analysis of the derivative nonlinear Schrödinger (DNLS) equation. And (1 + 1) dimensional fifth-order nonlinear Korteweg-de Vries (fKdV) type equations were obtained. So, we have demonstrated the relationship between the KdV equations and the DNLS-type equation.

Qualitative and Numerical Analysis to a Time-Fractional Stefan Convection-Diffusive Model Using Riemann-Liouville and Caputo Operators

2024-12-05T15:14:41+03:00

The importance of the time-fractional Stefan problem(SP) comes from its wide physical applications. In this study, we assume an advective-diffusive flux to derive the model of the fractional SP for linear advection and diffusion forces depending on a realistic ice-melting problem. The rescaling technique is significant in estimating the self-similar solutions for the Stefan model. Also, we consider the interface function to satisfy the time fractional SP including boundary and Stefan conditions. The fractional derivative method, particularly Riemann-Liouville and Caputo derivatives, is used to find approximated solutions. The SP and other related phase transition problems typically have a constitutive relation between quantity, enthalpy, and temperature that requires thorough derivation based on physical grounds. Since physical understanding requires mathematical analysis, we provide analytical formulas for weak solutions to the SP because the classical analytical approaches break down in the case of the changing interface. On the other hand, the time-fractional diffusion-convection equation is considered to estimate an approximated numerical solution by applying the Sumudu decomposition method (SDM). The proposed method depends on applying the Sumudu transform of the Caputo fractional derivative operator and then using the fractional integral of Riemann-Liouville. These processes are useful in handling the nonlinear term with ease. It is discovered that the Sumudu approach is precise and quick. The MATLAB software carried out all the computations and graphics. To show that the suggested technique is valid and applicable, illustrative examples are provided.

Comparison between the performance efficiencies of reverse osmosis and nanofiltration membrane systems in removing heavy metal ions from industrial wastewater

2025-01-22T09:11:15+03:00

Toxic contaminants that impact the health of humans and other animals include industrial wastewater, including cadmium, cobalt, chromium, and lead ions. To protect the environment, technologies such as “Reverse osmosis” (RO) and “Nanofiltration” (NF) membrane systems efficiently remove these ions from industrial effluent. Industrial wastewater samples were generated at room temperature and treated with both membrane systems in the laboratory. The samples contained Cd, Pb, Cr, and Co ions at concentrations ranging from 10 to 500 ppm, pressures ranging from 3 to 11 bar, and pH levels ranging from 4±0.2 to 7±0.2. Based on the findings, the RO system was able to remove Pb, Cd, Co, and Cr ions with efficiency of 98.55%, 97.97%, 97.308%, and 97.106%, respectively, when operated under the following conditions: pH = 6±0.2, pressure = 11 bar, pollutants concentrations = 500 ppm, time =
90 min at 25±2 °C. Operating parameters included a pH of 6±0.2, a pressure of 11 bar, a concentration of pollutants of 500 ppm, a duration of 90 minutes at 25±2 °C, and removal efficiencies of 96.37 percent for Pb, 95.44 percent for Cd, 94.478 percent for Co, and 93.965 percent for Cr in the (NF) system.