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The manuscript introduces the concept of a double-composed metric-like space, which is an extension of the notion of a double-composed metric space. In this new space, the self-distance is not necessarily zero, but if the distance metric equals zero, it must be for identical points of distance. Furthermore, this paper presents several results related to this novel concept in the literature, with a particular focus on Hardy–Rogers type contractions. It establishes fixed point theorems accompanied by some illustrative examples that elucidate the findings. Finally, this research provides an application to nonlinear integral equation to substantiate our theorems. [ABSTRACT FROM AUTHOR]

The multi-term time-fractional order diffusion-wave equation (MT-TFDWE) is an important mathematical model for processes exhibiting anomalous diffusion and wave propagation with memory effects. This article develops a robust numerical technique based on the Chebyshev collocation method (CCM) coupled with the Laplace transform (LT) to solve the time-fractional diffusion-wave equation. The CCM is utilized to discretize the spatial domain, which ensures remarkable accuracy and excellent efficiency in capturing the variations of spatial solutions. The LT is used to handle the time-fractional derivative, which converts the problem into an algebraic equation in a simple form. However, while using the LT, the main difficulty arises in calculating its inverse. In many situations, the analytical inversion of LT becomes a cumbersome job. Therefore, the numerical techniques are then used to obtain the time domain solution from the frequency domain solution. Various numerical inverse Laplace transform methods (NILTMs) have been developed by the researchers. In this work, we use the contour integration method (CIM), which is capable of handling complex inversion tasks efficiently. This hybrid technique provides a powerful tool for the numerical solution of the time-fractional diffusion-wave equation. The accuracy and efficiency of the proposed technique are validated through four test problems. [ABSTRACT FROM AUTHOR]

The computational study of fixed-point problems in distance spaces is an active and important research area. The purpose of this paper is to construct a new iterative scheme in the setting of Banach space for approximating solutions of fixed-point problems. We first prove the strong convergence of the scheme for a general class of contractions under some appropriate assumptions on the domain and a parameter involved in our scheme. We then study the qualitative aspects of our scheme, such as the stability and order of convergence for the scheme. Some nonlinear problems are then considered and solved numerically by our new iterative scheme. The numerical simulations and graphical visualizations prove the high accuracy and stability of the new fixed-point scheme. Eventually, we solve a 2D nonlinear Volterra Integral Equation (VIE) via the application of our main outcome. Our results improve many related results in fixed-point iteration theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of elliptic-valued b-metric spaces, extending the notions of elliptic-valued metric spaces and complex-valued metric spaces. We present several fixed-point results that involve rational and product terms within this novel space framework. To support our main findings, we offer numerical examples. Additionally, we demonstrate an application of Urysohn integral equations. [ABSTRACT FROM AUTHOR]

This article introduces the concept of generalized (ff F , b , ϕ ˘) contraction in the context of b -metric spaces by utilizing the idea of F contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existence of best proximity points for multi-valued (ff F , b , ϕ ˘) contractions in partially ordered b -metric spaces. The article provides examples to illustrate the main results and demonstrates the existence of solutions to a second-order differential equation and a fractional differential equation using the established theorems. Additionally, several corollaries are presented to show that the results generalize many existing fixed-point and best proximity point theorems. [ABSTRACT FROM AUTHOR]

In this publication, our objective was to introduce and establish the concepts of KGm-contraction and generalized (a, KGm)-contraction in complete Gm-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis. [ABSTRACT FROM AUTHOR]

In this manuscript, utilizing interpolative contractions with fractional forms, some unique fixed-point results were studied in the context of extended b-metric spaces. For the validity of the presented results some examples are given. In the last section an existence theorem is provided to study the existence of a solution for the Fredholm integral equation. [ABSTRACT FROM AUTHOR]

Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation. [ABSTRACT FROM AUTHOR]

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β -neighborhoods (IHF β -neighborhoods) and intuitionistic hesitant fuzzy complementary β -neighborhoods (IHFC β -neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β -neighborhoods and IHFC β -neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. [ABSTRACT FROM AUTHOR]