Results in Nonlinear Analysis

Transformation solution for Korteweg-de Vries equation with small delay

Laheeb Muhsen, Ahmed Bakheet, Esam A. Alnussairy — Tue, 22 Apr 2025 00:00:00 +0300

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, Bharti Yadav, Pooja Vats, Raksha Sharma — Sat, 31 May 2025 00:00:00 +0300

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, Abdelbasset Felhi, Irshad Ayoob, Nabil Mlaiki — Sat, 31 May 2025 00:00:00 +0300

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, Lorena López, Luz Rodríguez — Sat, 31 May 2025 00:00:00 +0300

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, Rajani Saini, Rahul Shukla — Sat, 31 May 2025 00:00:00 +0300

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, Tomofumi Matsuzawa — Sat, 31 May 2025 00:00:00 +0300

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, M.M. Shanmugapriya — Sat, 31 May 2025 00:00:00 +0300

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.