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Universal Journal of Mathematics and Applications
Scopus
ISSN 2619-9653 · Emrah Evren KARA · 196 articles in the index
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Journal Article
On Generalized Metallic Leonardo Numbers: Silver, Bronze, and Copper Cases
In this article, we discuss three new extensions of the Leonardo numbers in a generalized way, which we call the generalized Silver, Bronze, and Copper Leonardo numbers that converge to the Silver, Bronze, and Copper ratios, unifying existing metallic Leonardo sequences. We investigate their…
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Journal Article
Agile Decision-Making in Unstable Markets: A Soft Set Paradigm with Temporal Weighting
Navigating volatile financial markets requires decision-making frameworks that synergize analytical rigor with real-time adaptability. Traditional models, reliant on static criteria and fixed weights, falter in dynamically evolving economic landscapes where the relevance of parameters like risk…
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Journal Article
Milne's Estimates via Conformable Fractional Multiplicative Integrals
This paper explores Milne’s inequality in the context of multiplicative conformable fractional integrals, a recent extension of classical fractional calculus rooted in non-Newtonian analysis. Leveraging recent developments in multiplicative calculus, we establish a new fundamental identity that…
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Journal Article
Solvability of Multi-Order $\psi$-Hilfer Fractional Langevin Equations with Infinite Delay in Weighted Phase Spaces
This work introduces a new class of fractional Langevin equations with infinite delay by incorporating generalized Hilfer derivatives within a weighted Banach space framework. Unlike existing studies that rely on standard Caputo or Hilfer operators without incorporating delay-weight interactions…
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Journal Article
Adams-Bashforth Scheme and Kayo-Kengne-Akgül Derivative: Connexion and Chaotic Modelling
In this paper, we propose a novel formulation of the Adams–Bashforth scheme for solving fractional differential equations (FDEs) involving the Caputo-type Kayo–Kengne–Akgül derivative. We first recall the formal definitions of this derivative and its associated integral, establishing their…
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Journal Article
$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs
Johnson Awolola defined the $\alpha$-level neutrosophic set in the year 2020. However, this definition is not useful for getting some realistic results. In order to generate more realistic and applicable results, we have introduced a new concept of the $\rho$-level NSs in the form of $\rho$-lower…
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Journal Article
Trapezoid Inequalities for Twice Differentiable Mappings
This study introduces a new identity to derive alternative results for the inequality in (1.1) and compares them with previous findings. Additionally, new trapezoid inequalities are developed using the convexity of second-order derivatives' absolute values.
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Journal Article
Iterative Approximation for Mean Nonexpansive Mappings in Uniformly Convex Spaces with a Fractional Volterra Application
This paper investigates fixed point theory for mean nonexpansive mappings in $p$-uniformly convex metric spaces. It first establishes the existence of fixed points together with a demiclosedness principle in this setting. Building on these foundations, the two-step Karakaya iteration scheme is…
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Journal Article
Generalized Error Bounds for Mercer-Type Inequalities in Fractional Integrals with Applications
Fractional integral inequalities have emerged as powerful and versatile tools in advancing both pure and applied mathematics in recent years. Numerous researchers have recently introduced various generalized inequalities involving fractional integral operators. In this paper, we develop new…
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Journal Article
Weddle's Inequality via Katugampola Fractional Integrals
Integral inequalities represent an important and ongoing area of study in mathematical understanding. Due to their extensive use in science, fractional calculus approaches have been the subject of a great deal of research recently. An important concept in fractional calculus is the Katugampola…
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Journal Article
Existence of Solutions for a Class of Nonlinear Boundary Value Problems with Caputo Fractional Derivatives
Our aim in this paper is to explore the existence of nonnegative solutions for a boundary value problem involving nonlinear Caputo fractional differential equations. The analysis begins with the formulation of superlinear and sublinear conditions, under which the Guo-Krasnosel'skii fixed point…
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Journal Article
On Dual Hyperbolic Narayana and Narayana-Lucas Hybrid Quaternions
In this present communication, we introduce the novel concepts of dual hyperbolic Narayana quaternions and dual hyperbolic Narayana-Lucas quaternions within the framework of hybrid numbers. We also explore the connections between these newly defined quaternions and examine the mathematical…
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Journal Article
Construction and Analysis of Smarandache Curves for Integral Binormal Curves in Euclidean 3-Space
This paper presents a detailed geometric analysis of Smarandache curves generated from integral binormal curves within three-dimensional Euclidean space. We provide a complete derivation of the Frenet apparatus encompassing tangent, normal, and binormal vectors, alongside curvature and torsion…
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Journal Article
Generating Hyperchaotic Attractor via the Sprott B System and Its Application in Highly Secure Voice Encryption
This paper presents a new 4D system constructed based on the well-known Sprott B system and characterized by high complexity. This system can display chaotic, hyperchaotic, periodic, and quasi-periodic behaviors for some parameter values. The findings demonstrate that the novel system can exhibit…
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Journal Article
On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences
The primary objective of this study is to construct a novel double sequence space by utilizing the domain of a 4-dimensional (4D) matrix in the space $\mathcal{L}_u$ of the absolutely summable double sequences defined via the well-known Catalan numbers. Within this framework, various algebraic and…
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Journal Article
A Study on the k-Mersenne and k-Mersenne-Lucas Sequences
In this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences have terms according to different…
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Journal Article
Some Novel Proximal Point Results and Applications
The current study provides significant findings on coincidence the best proximity points for proximal-contractions in the context of extended $b$-metric spaces. To substantiate our assertions, we present illustrative examples across several circumstances. The conclusions presented in this study…
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Journal Article
New Analytical Wave Structures for the (2+1)-Dimensional Chaffee-Infante Equation
The focus of this paper is the (2+1)-dimensional Chaffee-Infante equation (CIE). The model describes the diffusion of a gas in a homogeneous medium, which makes it an important tool in the research of mathematics and physics. The modified extended Tanh expansion method is employed. Many soliton…
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Journal Article
On New Sequences of $p$-Binomial and Catalan Transforms of the $k$-Mersenne Numbers and Associated Generating Functions
In this work, we investigate the binomial transforms and Catalan transform of the $k$-Mersenne and $k$-Mersenne-Lucas numbers and examine the new integer sequences. We apply the $p$-binomial, rising $p$-binomial, and falling $p$-binomial transforms to the $k$-Mersenne sequences and present the…
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Journal Article
Solvability of Infinite Systems of Third Order Differential Equations in a Sequence Space $n ( \phi)$ via Measures of Non-Compactness
This paper establishes the necessary conditions for the existence of $\omega$-periodic solutions in the sequence space $n(\phi)$ for an infinite system of third-order differential equations. The analysis utilizes the system's Green's function, the Meir-Keeler condensing operator, and measures of…