Results in Nonlinear Analysis

The Mixed Slicing Structure Property

Daher AlBaydli — 2023-12-02

The aim of this paper is to structure a new concept of Mixed Slicing
Structure-Property denoted by (MSSP via short) and we give proof of the
mixed fibration is not mixed Hurewics fibration.

F(a0, a1, ...., an)-structures on manifolds

Mohammad Nazrul Islam Khan — 2023-12-02

The aim of the present paper is to study the geometry of n-dimensional
differentiable manifolds endowed with F(a0, a1, ...., an)-structure satisfying
anFn +an-1Fn-1+.......+a1F+a0I = 0 and establish its existence. Also, it is
proved that for the complex numbers, the dimension of a manifold M endowed
with F(a0, a1, ...., an)-structure is even. Furthermore, we study the Nijenhuis
tensor of a tensor field F of type (1,1) satisfying the general quadratic equation, which is a particular case of the F(a0, a1, ......, an)-structure. At last, we study the integrability conditions of an F(a0, a1, ......, an)-structure.

Vieta-Lucas Spectral Collocation Method for Solving Fractional Order Volterra Integro-differential Equations.

Mustafa Khirallah — 2023-12-02

The shifted Vieta-Lucas polynomial approach is taken into account for the numerical solution of linear and nonlinear fractional-order integro-differential equations of the Volterra type. Fractional derivatives are described in the Caputo sense. The suggested method reduces the complexity of these problems to the linear or nonlinear solution of algebraic equations. The convergence of the recommended strategy is studied in detail. The computing efficiency of this approach is then illustrated with certain numerical examples, and a comparison with prior research is made.

Prediction the biodegradation rate of soil contaminated with different oil concentrations

Andrey Lipatov — 2023-12-02

A multiple linear regression model is a practical statistical model for estimating relationships between a continuous dependent variable and predictor variables. The model itself is linear in that it consists of additive terms, each representing a predictor multiplied by an estimate of the coefficient. In addition, a constant (free term) is usually added to the model as well. Using two bacterial species (wild and recombinant), this paper develops a multiple model linear regression model to predict the biodegradation rate of soil contaminated with different oil concentrations. Factors such as crude oil concentration, number of days of incubation, and type of microbial strain were discovered to significantly influence the biodegradation rate based on visual and mathematical analysis. Mathematical models were developed to predict the biodegradation rate. The equation developed using multiple linear regression predicted the biodegradation rate with a coefficient of determination R2=0.549. The equation developed using polynomial regression predicted the biodegradation rate with a coefficient of determination R2=0.799. The resulting equations can be used to understand the relationship between the variables and also to predict the biodegradation rate of petroleum products.

Fixed point theorems in generalized b-Menger spaces

Rachid OUBRAHIM — 2023-12-07

The purpose of this work is to define the generalized b-Menger spaces and prove a fixed point theorem in this new setting. As application, we establish the existence and uniqueness of a solution for Volterra type integral equation.

GENERALIZED CAPUTO-KATUGAMPOLA FOR SOLVING FUZZY FRACTIONAL HEAT EQUATION

Abdallah Alshbeel — 2023-12-07

The fuzzy theory is investigated in this paper and the frac-
tional derivative with two parameters is used to construct the solution
of the fuzzy fractional heat equation. We devised a method for comput-
ing a semi-analytical solution to a fuzzy fractional-order heat equation
based on the Optimal Homotopy Asymptotic Method (OHAM). This
method helps us to overcome the obstacles and constraints that other
approaches impose whereby it is used to construct powerful and efficient
ways of finding the solutions to the heat equation with more accuracy,
minimal effort, and iterations. The Mittag–Leffler (ML) kernels which
include two parameters Eσ
ν,ξ (λ, s) are utilized to define the fractional
derivative. A broad approach to dealing with this type of situation is
presented. Several examples are provided to validate the outcome, which
is then contrasted with the precise solution to demonstrate the effective-
ness and feasibility of the proposed method. The results are presented
in terms of tables and figures

Approximate Polynomial Solution for Two-Point Fuzzy Boundary Value Problems

Mazin H. Suhhiem — 2023-12-20

In this research, we have used double decomposition method to find approximate analytical solutions for the two-point fuzzy boundary value problems. This method is based on the standard Adomian decomposition method, which is an approximation method that is used to solve fuzzy and non-fuzzy differential equations. This method allows for the solution to be calculated as a convergent series, This means that the solution is in the form of a polynomial that approaches the exact solution of the differential equation. The numerical solutions that we presented during this research showed the high efficiency of this method.

Variance estimator for Repeated Measurements Model by iterated bootstrap with an application to Oil industry pollutants in Basrah

Hadeel Ismail Mustafa — 2023-12-25

The aim of this research deals with the study of the estimators of the variance compounds by the bootstrap approximate method of the one-way repeated measurements (RM) model and the calculation of the amount of bias in the estimators of the variance components. The model contains two fixed factors (one factor within units and one factor between units) and their interactions and two random factors. As an applied aspect, a study was undertaken to measure the air pollutants (CO, CO2, and CH4) in the Al-Shuaiba region – Basrah in Iraq to study the variation in pollutant concentrations in two randomly selected stations from the region with five sections with two directions for each station during the summer and winter seasons 2019-2020. The SPSS statistical analysis program was used to analyze the study data and calculate the amount of bias in the estimators of the variance components.

Modeling the dynamics of a marine system using the fractional order approach to assess its susceptibility to global warming

R.N. Premakumari — 2023-12-30

In the marine ecosystem, phytoplankton plays a vital role as the primary supplier of oxygen, contributing to 50\% of the total oxygen production. Not only does it serve as a significant source of food for other species, but it also sustains life in the ocean. However, the rising ocean temperatures caused by global warming have severely hindered the ability of phytoplankton to generate oxygen. Furthermore, fishes are crucial consumers of oxygen within the marine ecosystem. This research paper presents a model that intricately connects the dynamics of oxygen, phytoplankton, zooplankton, and fish using the Caputo fractional derivative. The model aims to examine the impact of global warming on the collective dynamics by considering the relationship between the rate of oxygen generation, temperature, and time. The paper establishes the existence and uniqueness of solutions and also analyzes the stability of equilibrium points. Numerical simulations are conducted to demonstrate the impact of fractional derivatives and global warming on oxygen depletion and species extinction.

Geometric Characterization of Pointwise Slant Curves

S. K. Srivastava — 2024-01-10

In the present paper, we study the characteristics of pointwise slant curves in a normal almost contact semi-Riemannian three-manifold N3. These curves are characterized by the pseudo-Riemannian scalar product between the normal vector at the curve and the reeb vector field of manifold N3. In this class of manifolds, curvature and torsion of such curves are determined. The Lancret of slant curves in manifold N3 is obtained. Additionally, pointwise slant curves with proper mean
curvature are characterized.

Some fixed point results in metric spaces equipped with a Graph and their applications

Reny George — 2024-01-11

In this paper, we define the notion of $(F-H)_G$- contraction and utilize the same to obtain fixed point results in the setting of metric spaces equipped with a graph. Our results generalizes many known fixed point results in literature. As an application, we investigate the existence and uniqueness of a solution of integral equation. Finally, some suitable examples are given to validate our claim.

Estimate the Shape Parameter for the Kumaraswamy Distribution via Some Estimation Methods

Sudad K. Abraheem — 2024-02-08

This paper shows how to estimate one of the two shape parameters of Kumaraswamy distribution using two estimation methods. The first one is the rank set sampling estimation method and the second one is the Bayes estimation method. The rank set sampling was employed as a non-Bayes estimator. In addition, Bayes estimators were used based on asymmetric loss function (LINEX) by utilizing four kinds of informative prior (one single prior and three double prior). Comparisons were made between different estimators using a Monte Carlo simulation study and the shape parameter estimates were compared depending on the mean squared error. Finally, the program (MATLAB 2015) was used to get the mathematical outcomes.

Mathematical analysis of a fractional order two strain SEIR epidemic model

Zakaria Yaagoub — 2024-02-09

In this paper, a fractional order two-strain SEIR epidemic model is studied and analyzed. This model will be presented in the form of a system containing six fractional order equations, that illustrate the interactions between susceptible, strain-1 exposed, strain-2 exposed, strain-1 infected, strain-2 infected and removed individuals. The proposed model has four equilibrium points: the disease-free equilibrium point, the strain-1 equilibrium point, the strain-2 equilibrium point and the total equilibrium point. By determining the new generation matrix, we have shown that our model has two basic reproduction numbers R1 0 and R2 0; the first one is associated with the strain-1and the second one is related to the strain-2. Using the Lyapunov method and La-Salle’s invariance principle, we have proved the global stability of the different equilibrium points, this stability depends on the strain-1 reproduction number R1 0 and on the strain-2 reproduction number R2 0. Finally, numerical simulations are presented to value our theoretical results. More precisely, if the two basic reproduction numbers are less than or equal 1, then the disease-free equilibrium point is globally asymptotically stable, if one of the basic reproduction numbers is less than or equal 1 and the other is greater than 1, then the equilibrium point associated with the greatest basic reproduction number is globally asymptotically stable, and if the two basic reproduction numbers are greater than 1, then the last equilibrium point is globally asymptotically stable. Moreover, we have shown that the change in the fractional order value has no effect on the stability of thesteady states. However, the time of convergence toward these states depends on the value of the fractional order derivative.

Exploring Maximal and Minimal Open Submsets in M-Topology: A Comprehensive Analysis

Baiju Thankachan — 2024-02-20

Topological structures defined in the context of multisets, a set that allows multiple occurrences of objects, are referred to as M-topological spaces. This article introduces the concept of maximal and minimal open submsets in M-topology. The role of whole elements and part elements in maximal open and minimal open submsets and their uniqueness, together with the topological situation in which an open submset becomes both maximal open and minimal open, is analysed. Some conditions for disconnectedness in M-topologyical spaces are obtained in light of the fact that the existence of a non-empty proper clopen submset is not enough to establish the disconnectedness of an M-topologyical space.