Results in Nonlinear Analysis

Transformation solution for Korteweg-de Vries equation with small delay

Laheeb Muhsen — 2025-04-22

In this paper we develop a new approach to get the transformation solution for the mathematical model of waves on shallow fluid; Korteweg-de Vries with a small delay without change the space variables. This method can be base to solve most of nonlinear higher order partial differential equation with time delay.

Bell Wavelet operational matrix method for convection diffusion equation

Shahid Ahmed — 2025-05-31

In this article, we introduce an efficient method using Bell wavelets to solve fractional-order convection-diffusion equations with variable coefficients and initial boundary conditions. We begin by integrating block pulse functions with the Bell wavelet matrix to construct the fractional-order operational matrix of integration (OMI). This method simplifies fractional models by converting them into a set of algebraic equations via the collocation technique. The Bell wavelet collocation technique results in an efficient computational approach characterised by low costs and rapid convergence. Four numerical examples are presented, and the results are compared with exact solutions and other existing methods to validate the method and demonstrate its effectiveness and applicability. Graphical results highlight significant variations between fractional and integer orders, while our method adeptly handles both initial and boundary conditions, enhancing overall accuracy and simple applicability.

On Huang-Samet multivalued p-contractions

Hassen Aydi — 2025-05-31

This paper is devoted to prove the existence of fixed points for some classes of multivalued maps in the context of metric spaces. The obtained results generalize the recent theorems of Huang and Samet. Some examples are presented making effective our results.

Second Bounded Variation in the Sense of Shiba with Variable Exponent

Ebner Pineda — 2025-05-31

In this paper we present the notion of second bounded variation in the sense of Shiba with variable exponent, studying the structure of these functions spaces, showing its basic properties and some inclusion results among them.

Common fixed point theorems for compatible maps in complex valued b - metric space

Vishal Gupta — 2025-05-31

The article investigates common fixed point theorems in the framework of complete complex-valued b -metric space. It establishes such theorems for compatible mappings and employs rational inequalities to derive novel results. These findings serve to extend and generalize existing results in the literature. To illustrate the practical applicability and effectiveness of the proposed methods, the article presents several non-trivial examples.

A version of Hilbert's 13th problem for infinitely differentiable functions

Shigeo Akashi — 2025-05-31

It is famous that Hilbert's 13th problem, asking if there exists a continuous real-valued function of multivariables which cannot be represented as any finite-time nested superposition of several functions of fewer variables, was proved by Kolmororov and Arnold. Actually, it is well known that there exist some other versions having been derived from the original one and still remaining to be open such as the analytic function version and the infinitely differentiable function version.

In this paper, we discuss a version of Hilbert's 13th problem for the infinitely differentiable functions. Exactly speaking, an example of an infinitely differentiable function of three real variables which cannot be represented as finite-time nested superposition of several infinitely differentiable functions of two real variables.

Eigen neutrosophic Z-set and neutrosophic Z-relation: A nonlinear dynamic modeling approach under uncertainty

P. Sheeba Maybell — 2025-05-31

The modelling and Analysis of nonlinear systems under uncertainty are particularly difficult in scientific and engineering discipline. In many problems involving real world complex data, the inherent indeterminacy, vagueness and partial truth value associated with various real world complex phenomena is difficult to effectively capture using traditional frameworks. This study presents a novel nonlinear dynamic modelling framework based on Eigen Neutrosophic Z-Set and Neutrosophic Z-Relations framework to systematically handle the above challenges. The mathematical foundations of Neutrosophic Z sets are set up and discrete time dynamical systems given by Neutrosophic relational compositions are formulated. Properties of stability are rigorously analysed and proofs that
convergence to fixed point eigen structures are derived. Details are presented of computational algorithms for determining Greatest Eigen Neutrosophic Z-Set (GENZS) and Least Eigen Neutrosophic Z-Set (LENZS). The theoretical framework is validated through the simulations on representative systems in which the numerically generated solutions accommodate the fast convergence and retain
the stability of the systems under variation of the uncertainty conditions. The proposed approach provides a powerful and general means of modelling the nonlinear systems subject to uncertainty and could be applied, for example, in the area of engineering design, decision making systems and complex socio-economic modelling.

Influence of weather elements on grapes growth, yield and disease incidence using Epidemiological modeling

M. Uma Maheswari — 2025-06-09

Mathematical models play a vital role in crop agriculture to understand, predict and forecast the yield and disease incidence. This paper explores the utilization of mathematical model in grapes based on non-steady state equations possessing a nonlinear term. Theoretically, evaluated non-steady state concentration of leaf surface area for optimal strategy for grapes system presented. The analytical results of this study found to be matching with numerical results using MATLAB pdex4 function. Further, the proposed model validated with the field level data collected from Theni district, Tamil Nadu. Disease incidence and yield of grapes were highly influenced by weather variables. In addition, important aspects like disease intensity, infection rate and number of diseased leaves for secondary and primary infection studied in detail.

Approximating to a common fixed point and a minimizer of a convex function in Hadamard spaces

Yasunori Kimura — 2025-07-03

This paper considers approximate sequences convergent to a common solution to a family of fixed point problems and convex minimization problems. We found that the lemma used to prove a known convergence theorem has a gap in its proof, and we obtained a counterexample. Further, we get an analogous result by substituting the convex combination of finitely many points by the balanced mapping.

Blow-Up Dynamics of Solutions to a Nonlinear Wave Equation with Positive Initial Energy

Begüm Çalışkan Desova — 2025-07-03

This paper investigates the dynamics of a quasi-linear partial differential equation of fourth order characterized by bi-hyperbolic properties, incorporating dynamic boundary conditions. The study focuses on the interplay between the equation's nonlinear source term, the boundary effects, and the initial energy. By applying the concavity method, we derive conditions that lead to the finite-time blow-up phenomenon in solutions with non-negative initial energy. These findings highlight the impact of dynamic boundary conditions on the development of finite-time singularities in higher-order hyperbolic equations.

The Monto-Carlo procedure of some estimation methods for Exponential-Weibull distribution

Israa A. Ahmed — 2025-06-28

In this paper, deicing and derivative two parameters of Exponential Weibull (EW) distribution using three methods of estimate first is maximum likelihood estimation (MLE) the second is ordinary least squares estimation (OLS) and the third is ranked set sampling estimation (RSSE). After that, the simulation technique (Monto-Carlo method) is used to estimate the parameters and Reliability function for different values of sample size and various values of initial values by employing a MATLAB programmer and then using the Mean square error to find which method is the best

Mathematical modeling and optimization of intelligent systems using a hybrid PSO-GWO algorithm: A minx J(x) approach

Jumana J. Al-zamili — 2025-06-28

In this paper, a comparative analysis of Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and a hybrid PSO-GWO algorithm for the solution of complex optimization problems have been presented. The hybrid algorithm consists of the exploitation strength of GWO and the exploration capabilities of PSO while combining both together to surmount the failure of standalone algorithms like slow convergence in GWO and premature convergence in the PSO. The algorithms were evaluated in terms of convergence speed, robustness, and accuracy, on a series of benchmark functions (Sphere, Rastrigin, Ackley, Rosenbrock, and Griewank). The results of simulations indicate that the notion of a hybrid PSO-GWO algorithm is always better compared to standalone PSO as well as GWO for lower mean square errors (MSE) and quicker convergence to global optimum for different optimization landscapes. Finally, the hybrid approach took advantage of the best in all three aspects to optimize multimodal, non-convex, and deceptive functions with both reliable and robust performance that was superior to that of local minimum avoidance algorithms. This research shows that the hybrid PSO-GWO algorithm is an efficient tool for robust optimization in the real-world systems of dynamic, complex systems. Future work is to extend the algorithm’s adaptability to real-world constraints, and dynamic parameter adjustment, and integrate it within domain-specific heuristics to improve the optimization in engineering and automation tasks.

Optimization of ordinary differential equations (ODE) solutions using modified recurrent neural networks

Aseel Najih Abbas Hassan Al-Maamouri — 2025-06-30

This paper introduces a hybrid approach for solving ordinary differential equations (ODE) using modified recurrent neural networks (mRNNs). The approach combines mRNNs with novel optimization techniques. Crucially, when training an mRNN, training data points should be selected from the open interval (a, b) to avoid training the network with the boundary points. This approach reduces computational errors by avoiding boundary region training. Furthermore, we propose a transformation that maps training points from a potentially broader interval [a, b] into corresponding points within the open interval (a, b), before training. This allows the network to be trained on points that are similar in the open interval, which leads to improved accuracy. The proposed model demonstrates higher
accuracy compared to existing mRNN models. A numerical example and corresponding simulations demonstrate the mathematical effectiveness of this approach.

Some Novel Versions of Fractional Hermite–Hadamard-Mercer Type Inequalities with Matrix Applications

Jamshed Nasir — 2025-07-08

In this study, we explore several fractional Hermite–Hadamard (H–H)-Mercer inequalities for interval-valued functions through the use of a generalized fractional integral operator (GFIO). Furthermore, we examine new variations of the H–H-Mercer inequality in relation to GFIO. Various examples are included to support our assertions. The results could offer new insights into a broad spectrum of integral inequalities for fractional fuzzy systems within the framework of interval analysis, along with the optimization issues they raise. Moreover, some applications on matrices are illustrated.

An extended iterative algorithm for solving nonlinear systems and differential equations

B. Sharmila — 2025-07-11

An extended iterative algorithm for solving nonlinear systems and ordinary differential equations (ODE) is presented in this paper which is efficient. Convergence difficulty, high computation cost and instability are the obstacles of using traditional methods like Newton method and explicit Runge-Kutta methods for stiff problems. In this approach proposed, we enhance numerical stability and bring about the convergence speed by introducing a modifed Jacobian matrix. To solve multi variable nonlinear systems, the algorithm is structured such that it adapts to a dynamically varied update step, which reduces the sensitivity toward the initial conditions. Furthermore, for ODEs we apply an implicit numerical integration combining with the modified Jacobian so that it is well suited to stiff and high dimensional systems. It is shown by theoretical analysis that the nonlinear equations converge superlinearly and numerical experiments are used to show that the methods perform better than classical approaches in terms of accuracy and efficiency. It is used for engineering simulations as well as machine learning optimization problems. The method will be extended to partial differential equations (PDEs) as future work, as will adaptively choosing the step size for further improvements in the computation