Axioms, Volume 13, Issue 9

This study contains a mathematical model for river pollution and its remediation for an unsteady state and investigates the effect of aeration on the degradation of pollutants. The governing equation is a pair of nonlinear time-fractional two-dimensi...

In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives...

This paper investigates the oscillatory behavior of solutions to fourth-order functional differential equations (FDEs) with multiple delays and a middle term. By employing a different comparison method approach with lower-order equations, the study i...

This editorial concerns the Special Issue of Axioms entitled “Advances in Difference Equations” [...]

This manuscript examines fuzzy fixed point results using the concepts of $\mathcal{S}$-metric space. We introduce two contractive maps, $\gamma$- and $\gamma$-weak contractions, within the context of $\mathcal{S}$-metric spaces. These contractive maps form the cornerstone of...

A theory for the calculation of the phase–lag and amplification–factor for explicit and implicit multistep techniques for first–order differential equations was recently established by the author. His presentation also covered how t...

The estimation of unknown quantities from multiple independent yet non-homogeneous samples has garnered increasing attention in various fields over the past decade. This interest is evidenced by the wide range of applications discussed in recent lite...

In the framework of linear viscoelasticity, the authors have previously calculated a novel inverse Laplace transform involving the Mittag–Leffler function in order to calculate the relaxation modulus in the Andrade model. Here, we generalize th...

In this paper, we investigate a two-dimensional singular fractional-order parabolic partial differential equation in the Caputo sense. The partial differential equation is supplemented with Dirichlet and weighted integral boundary conditions. By empl...

In this manuscript, we will discuss the solutions of Goursat problems with fuzzy boundary conditions involving gH-differentiability. The solutions to these problems face two main challenges. The first challenge is to deal with the two types of fuzzy...

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of sin...

In periods of dramatic stock price volatility, the identification of change points in stock price time series is important for analyzing the structural changes in financial market data, as well as for risk prevention and control in the financial mark...

In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The pa...

There has been increasing interest in best–worst discrete choice experiments (BWDCEs) in health economics, transportation research, and other fields over the last few years. BWDCEs have distinct advantages compared to other measurement approach...

In this paper, a nonlinear dynamic equation with an initial value problem (IVP) on a time scale is considered. First, applying comparison results with a coupled lower solution (LS) and an upper solution (US), we improved the quasilinearization method...

In this study, we investigate the concept of $I^{*}$-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship betw...

In numerous scientific and engineering domains, fractional-order derivatives and integral operators are frequently used to represent many complex phenomena. They also have numerous practical applications in the area of fixed point iteration. In this...

The red palm weevil (Rhynchophorus ferrugineus) is a highly destructive pest, causing severe damage to palm trees and significantly reducing their productivity. This paper aims to develop and analyze a mathematical model that captures the interaction...

This paper investigates generalized Robertson–Walker (GRW) spacetimes by analyzing Riemannian hypersurfaces within pseudo-Riemannian warped product manifolds of the form $(\overline{M},\overline{g})$, where $\overline{M}=\mathbb{R}{\times }_{f}M$ and $\overline{g}=ϵd{t}^2+f^2(t)g_M$...

Let ${\Phi }_i(i=1,2)$ be two N-functions, f be a $\mu$-measurable function, and ${\omega }_i(i=1,2,3,4)$ be four weight functions. This study presents necessary and sufficient conditions for weight functions $({\omega }_1,{\omega }_2,{\omega }_3,{\omega }_4)$ such that the...

This study addresses the state feedback control associated with D-admissible assurance for discrete singular systems subjected to parameter uncertainties in both the difference term and system matrices. Firstly, a refined analysis criterion of D-admi...

This research explores the interplay between violator spaces and greedoids—two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to...

Vertex-degree-based (VDB) topological indices have been applied in the study of molecular structures and chemical properties. At present, the exponential VDB index has been studied extensively. Naturally, we began to consider the logarithmic VDB inde...

This paper investigates Parseval–Goldstein-type relationships in the framework of Lebedev–Skalskaya transforms. The research also examines the continuity properties of these transforms, along with their adjoint counterparts over weighted...

We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying...

The ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter p between zero and one. Several variations of the ERW model have recently b...

Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. This class has been investigated by many authors, mainly to find the co...

In this research paper, we consider a model of the fractional Cauchy–Euler-type equation, where the fractional derivative operator is the Caputo with order $0<\alpha <2$. The problem also constitutes a class of examples of the Cauchy proble...

Aiming to explore the subtle connection between the number of nonlinear terms in Lorenz-like systems and hidden attractors, this paper introduces a new simple sub-quadratic four-thirds-degree Lorenz-like system, where $\dot{x}=a(y-x)$, $\dot{y}=cx$...

In this paper, we introduce and rigorously define a novel class of difference sequence spaces, denoted by $w^{\mathcal{I}}{(\mathcal{M},{∆}_v^u,r)}_{\alpha }^{\beta }$, $w_0^{\mathcal{I}}{(\mathcal{M},{∆}_v^u,r)}_{\alpha }^{\beta }, w_{\infty }^{\mathcal{I}}{(\mathcal{M},{∆}_v^u,r)}_{\alpha }^{\beta }$, and $w_{\infty }{(\mathcal{M},{∆}_v^u,r)}_{\alpha }^{\&}$...

The key point in the process of agent-based management in e-service for malware detection (according to accuracy criteria) is a decision-making process. To determine the optimal e-service for malware detection, two concepts were investigated: Fuzzy L...

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equat...

In this article, we study the properties of 4-by-4 metric matrices and characterize their dependence and independence by ${\mathcal{M}}^{4\times 4}=({\mathcal{M}}^{4\times 4}-D{\mathcal{M}}^{4\times 4})\cup D{\mathcal{M}}^{4\times 4}$, where $D{\mathcal{M}}^{4\times 4}$ is the set of all dependent metric matrices. $D{\mathcal{M}}^{4\&tim}$...

A quadratic integral Equation (QIE) of the second kind with continuous kernels is solved in the space $C\left(\right[0,T]\times [0,T\left]\right).$ The existence of at least one solution to the QIE is discussed in this article. Our evidence depends on a suitable combination...

Sălăgean differential operator ${\mathbb{D}}^{\kappa }$ plays an important role in the geometric function theory, where many studies are using this operator to introduce new subclasses of analytic functions defined in the open unit disk. Studies of Să...

Within the framework of symmetric teleparallel $f\left(Q\right)$-gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler–DeWitt equation of quantum cosmology. The gravitational field equation in $f\left(Q\right)$-gravity permits a minisupersp...

To solve complex multi-attribute decision-making (MADM) problems within a triangular dual hesitant fuzzy (TDHF) environment where the attribute weights (Aws) are either fully or partially known, a novel bidirectional projection method is proposed, na...

This paper aims to introduce a new fractional extension of the interval Hermite–Hadamard ($\mathcal{H}\mathcal{H}$), $\mathcal{H}\mathcal{H}$–Fejér, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings ($\mathcal{L}\mathsf{R}\mathsf{I}\mathsf{V}\mathsf{H}$ convex mappings) with...

In this paper, we present two different ways for computing the Kauffman bracket skein module of $S^1\times S^2$, $\mathrm{KBSM}\left(S^1\times S^2\right)$, via braids. We first extend the universal Kauffman bracket type invariant V for knots and links in the Solid Torus ST, which...

Regarding round-off errors as random is often a necessary simplification to describe their behavior. Assuming, in addition, the symmetry of their distributions, we show that one can, in unstable (ill-conditioned) computer calculations, suppress their...

In this paper, we investigate and characterize a family of optimization problems introduced by interval-valued functionals that are determined by curvilinear integrals. To this end, we first state the path independence and (strictly) $LU$ convexity pro...

By anchoring the lower rollers and dynamically adjusting the upper roller’s downfeed of a pyramid roll bender, one can achieve the precise bending of a workpiece into a desired planar form characterized by variable curvature. To ensure the seam...

In this paper, we investigate the spatial quaternionic expressions of partner-ruled surfaces. Moreover, we formulate the striction curves and dralls of these surfaces by use of the quaternionic product. Furthermore, the pitches and angles of pitches...

This paper concerns control BVPs, driven by ODEs $x^{\prime }\left(t\right)=u\left(t\right)$, using controls $u^0\left(·\right)$ $\&u^1\left(·\right)$ in $L^1\left(\left(a,b\right),{\mathbb{R}}^2\right)$. We ask these two controls to satisfy a very simple restriction: at points where their first coordinates coincide, also their se...

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a...

The aim of this research article is to broaden the scope of fixed point theory in $\mathfrak{F}$-bipolar metric spaces by introducing the concept of rational ($⋏,⋎,\psi$)-contractions. These new contractions allow for the formulation of fixed point the...

Many people, including Horadam, have studied the numbers $W_n$, satisfying the recurrence relation $W_n=u{W}_{n-1}+v{W}_{n-2}$ ($n\ge 2$) with $W_0=0$ and $W_1=1$. In this paper, we study the p-numerical semigroups of the triple $(W_i,W_{i+2},W_{i+k})$ for integers $i,k(\&$...

Symmetric spaces and $sn$-symmetric spaces, as a generalization of metric spaces, have many important properties and have been widely discussed. We consider characterizations and mapping properties of $sn$-symmetric spaces under ideal convergence. $\mathcal{I}$-symm...

In this paper, we review and compare the stochastic quantum mechanics of Nelson and the scale relativity theory of Nottale. We consider both nonrelativistic and relativistic frameworks and include the electromagnetic field. These theories propose a d...

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann–Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequ...