https://nonlinear-analysis.com/index.php/pub/issue/feedResults in Nonlinear Analysis2025-05-31T13:27:42+03:00Inci M. Erhaneditor@nonlinear-analysis.comOpen Journal Systems<p><strong>Dear Authors,</strong></p> <p>We are pleased to announce a new scientific journal, in the research field of nonlinear analysis, that was founded at the end of January 2018. It is titled <strong>R</strong>esults in <strong>N</strong>onlinear <strong>A</strong>nalysis<strong>(RNA)</strong> with ISSN 2636-7556</p> <p>It is an <strong>open-access</strong> journal, which published only in electronic form.</p> <p>It is quarterly published journal ( 4 issues in each volume)</p> <p>The aim is to publish outstanding theoretical and applicable results connected with nonlinear analysis. Besides research papers of significant interest, we would also accept surveys from leading mathematicians on various theory areas of nonlinear analysis.</p> <p>For the first year’s issues, we would encourage authors to submit their papers to any member of the editorial board.</p>https://nonlinear-analysis.com/index.php/pub/article/view/568Transformation solution for Korteweg-de Vries equation with small delay2025-03-03T13:20:12+03:00Laheeb Muhsenlaheeb_muhsen@yahoo.comAhmed Bakheetahmedbakheet@uomustansiriyah.edu.iqEsam A. Alnussairyeahmed@uowasit.edu.iq<p>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.</p>2025-04-22T00:00:00+03:00Copyright (c) 2025 Results in Nonlinear Analysishttps://nonlinear-analysis.com/index.php/pub/article/view/544Bell Wavelet operational matrix method for convection diffusion equation2025-02-06T11:35:05+03:00Shahid Ahmedchshahid9092@gmail.comBharti Yadavbhartiyadav4170@gmail.comPooja Vatspoojavats@krmangalam.edu.inRaksha Sharmarakshakmc@gmail.com<p>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.</p>2025-05-31T00:00:00+03:00Copyright (c) 2025 Results in Nonlinear Analysishttps://nonlinear-analysis.com/index.php/pub/article/view/615On Huang-Samet multivalued p-contractions2025-03-03T14:12:06+03:00Hassen Aydihassen.Aydi@isima.rnu.tnAbdelbasset Felhiabdelbassetfelhi@gmail.comIrshad Ayoobiayoub@psu.edu.saNabil Mlaikinmlaiki@psu.edu.sa<p>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.</p>2025-05-31T00:00:00+03:00Copyright (c) 2025 Results in Nonlinear Analysishttps://nonlinear-analysis.com/index.php/pub/article/view/467Second Bounded Variation in the Sense of Shiba with Variable Exponent2024-12-05T15:06:02+03:00Ebner Pinedaepineda@espol.edu.ecLorena Lópezlorena.lopez@ucla.edu.veLuz Rodríguezluzeurod@espol.edu.ec<p>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.</p>2025-05-31T00:00:00+03:00Copyright (c) 2025 Results in Nonlinear Analysishttps://nonlinear-analysis.com/index.php/pub/article/view/441Common fixed point theorems for compatible maps in complex valued b - metric space2024-08-04T14:47:44+03:00Vishal Guptavishal.gmn@gmail.comRajani Sainiprof.rajanisaini@gmail.comRahul Shuklarshukla.vnit@gmail.com<p>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.</p>2025-05-31T00:00:00+03:00Copyright (c) 2025 Results in Nonlinear Analysishttps://nonlinear-analysis.com/index.php/pub/article/view/634A version of Hilbert's 13th problem for infinitely differentiable functions2025-03-15T23:11:38+03:00Shigeo Akashiakashi.sub@gmail.comTomofumi Matsuzawat-matsu@is.noda.tus.ac.jp<p>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.</p> <p>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.</p>2025-05-31T00:00:00+03:00Copyright (c) 2025 Results in Nonlinear Analysishttps://nonlinear-analysis.com/index.php/pub/article/view/666Eigen neutrosophic Z-set and neutrosophic Z-relation: A nonlinear dynamic modeling approach under uncertainty 2025-05-28T09:38:22+03:00P. Sheeba Maybellsheeba.maybell@gmail.comM.M. Shanmugapriyapriya.mirdu@gmail.com<p>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 <br>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 <br>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.</p>2025-05-31T00:00:00+03:00Copyright (c) 2025