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In this manuscript, we prove new extensions of Nashine, Wardowski, Feng-Liu, and Ćirić-type contractive inequalities using orbitally lower semi-continuous functions in an orbitally complete bb-metric space. We accomplish new multivalued common fixed point results for two families of dominated set-valued mappings in an ordered complete orbitally bb-metric space. Some new definitions and illustrative examples are given to validate our new results. To show the novelty of our results, applications are given to obtain the solution of nonlinear integral and fractional differential equations. Our results expand the hypothetical consequences of Nashine et al. (Feng–Liu-type fixed point result in orbital b-metric spaces and application to fractal integral equation, Nonlinear Anal. Model. Control. 26 (2021), no. 3, 522–533) and Rasham et al. (Common fixed point results for new Ciric-type rational multivalued-contraction with an application, J. Fixed Point Theory Appl. 20 (2018), no. 1, Paper No. 45).

A model describing the transmission dynamics of cholera is considered in this article. The concerned model is investigated under the Caputo-Fabrizio fractal fractional derivative. The objective of this article is to study theoretical and numerical results for the model under our consideration. Classical fixed point approach is used to obtain sufficient conditions for the existence of solution to the proposed model. Adam’s Bashforth numerical method is utilized for the numerical interpretation of the suggested model. The considered technique is a powerful mathematical tool, that provides a numerical solution for the concerned problem. To discuss the transmission dynamics of the considered model, several graphical presentations are given.

Modeling several physical events leads to the Bagley–Torvik equation (BTE). In this study, we have taken into account the BTE, including the Caputo–Fabrizio and Atangana–Baleanu derivatives. It becomes challenging to find the analytical solution to these kinds of problems using standard methods in many circumstances. Therefore, to arrive at the required outcome, numerical techniques are used. The Laplace transform is a promising method that has been utilized in the literature to address a variety of issues that come up when modeling real-world data. For complicated functions, the Laplace transform approach can make the analytical inversion of the Laplace transform excessively laborious. As a result, numerical techniques are utilized to invert the Laplace transform. The numerical inverse Laplace transform is generally an ill-posed problem. Numerous numerical techniques for inverting the Laplace transform have been developed as a result of this challenge. In this article, we use the Weeks method, which is one of the most efficient numerical methods for inverting the Laplace transform. In our proposed methodology, first the BTE is transformed into an algebraic equation using Laplace transform. Then the reduced equation solved the Laplace domain. Finally, the Weeks method is used to convert the obtained solution from the Laplace domain into the real domain. Three test problems with Caputo–Fabrizio and Atangana–Baleanu derivatives are considered to demonstrate the accuracy, effectiveness, and feasibility of the proposed numerical method.

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model that highlights the significance of delay in its effectiveness. Time delays can affect the nature of patterns and slow down the emergence of patterns in infected population density. The analyzed model is expanded with the equilibrium analysis, reproduction number, and stability analysis. This study aims to establish and explore the non-standard finite difference (NSFD) scheme for the typhoid fever virus transmission model with a time delay. In addition, the forward Euler method and Runge-Kutta method of order 4 (RK-4) are also applied in the present research. Some significant properties, such as convergence, positivity, boundedness, and consistency, are explored, and the proposed scheme preserves all the mentioned properties. The theoretical validation is conducted on how NSFD outperforms other methods in emulating key aspects of the continuous model, such as positive solution, stability, and equilibrium about delay. Hence, the above analysis also shows some of the limitations of the conventional finite difference methods, such as forward Euler and RK-4 in simulating such critical behaviors. This becomes more apparent when using larger steps. This indicated that NSFD is beneficial in identifying the essential characteristics of the continuous model with higher accuracy than the traditional approaches. [ABSTRACT FROM AUTHOR]

The technique to broaden the scope of fixed point theory is to extend the class of spaces that have stronger conceptual frameworks than metric spaces. Therefore, this paper explores the introduction of novel metric spaces, namely, Branciari suprametric spaces, and investigates some of its fundamental topological properties. An illustration is provided to validate the newly defined idea of Branciari suprametric spaces. Further two intriguing, fixed point results are proved, and a corollary is presented as an implication of our main result. The following is a specification of the analogue of the rectangle inequality in Branciari suprametric spaces dB (τ,ι) ≤ dB (τ,ν)+dB(ν,σ)+dB(σ,ι) + μdB (τ,ν)dB(ν,σ)dB(σ,ι) for all t≠v, v≠σ and σ≠1. Furthermore, by employing the results obtained, the present study intends to provide an appropriate solution for the nonlinear fractional differential equations of the RiemannLiouville type. [ABSTRACT FROM AUTHOR]

The paper presents a detailed analysis of control and observation of generalized Caputo proportional fractional time-invariant linear systems. The focus is on identifying controllable states and observable systems within the controllable subspace, null space, and unobservable subspace of the proposed system. The necessary conditions for the controllable subspace and the necessary and sufficient conditions for observability criteria are firmly established. The controllable subspace is treated geometrically as the set of controllable states, while the observable system is characterized by a zero unobservable subspace. The results are reinforced by examples and will immensely benefit future studies on fractional-order control systems. [ABSTRACT FROM AUTHOR]

In the past, the existence and uniqueness of the solutions of fractional differential equations have been investigated by many researchers theoretically in various approaches in the literature. In this paper, there is no discussion of the existence of solutions for the nonlinear differential equations with fractal fractional operators. The objective of this work is to present novel contraction approaches, notably the α-φ-contraction α-type of the F-contraction, within the context of F-metric and orbital metric spaces. The aim of this study is to illustrate certain fixed point theorems that offer a new and direct approach to establish the existence and uniqueness of the solution to the general partial differential equations by employing the fractal fractional operators. [ABSTRACT FROM AUTHOR]

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,μ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory. [ABSTRACT FROM AUTHOR]

Clinical decision-making in chronic disorder prognosis is often hampered by high variance, leading to uncertainty and negative outcomes, especially in cases such as chronic kidney disease (CKD). Machine learning (ML) techniques have emerged as valuable tools for reducing randomness and enhancing clinical decision-making. However, conventional methods for CKD detection often lack accuracy due to their reliance on limited sets of biological attributes. This research proposes a novel ML model for predicting CKD, incorporating various preprocessing steps, feature selection, a hyperparameter optimization technique, and ML algorithms. To address challenges in medical datasets, we employ iterative imputation for missing values and a novel sequential approach for data scaling, combining robust scaling, z-standardization, and min-max scaling. Feature selection is performed using the Boruta algorithm, and the model is developed using ML algorithms. The proposed model was validated on the UCI CKD dataset, achieving outstanding performance with 100% accuracy. Our approach, combining innovative preprocessing steps, the Boruta feature selection, and the k-nearest neighbors algorithm, along with a hyperparameter optimization using grid-search cross-validation (CV), demonstrates its effectiveness in enhancing the early detection of CKD. This research highlights the potential of ML techniques in improving clinical support systems and reducing the impact of uncertainty in chronic disorder prognosis. [ABSTRACT FROM AUTHOR]

In this article, we present the use of a unique and common fixed point for a pair of mappings that satisfy certain rational-type inequalities in complex-valued b-metric spaces. We also provide applications related to authenticity concerns in integral equations. Our results combine well-known contractions, such as the Ćirić contraction and almost contractions. [ABSTRACT FROM AUTHOR]

In this paper, we study the results of fixed points for the operator equations of type x = H (ϝ x , x) using the idea of measure of noncompactness and assuming that the operator ϝ is k -set contractive (strictly k -set contractive, or a continuous) and the family { H (u ,.) : u } is equiexpansive or equicontractive. The obtained results are generalization of Krasnoselskii type fixed point results. Some examples are given to elaborate new concepts. We use the main result to find the existence of solutions for the stationary radiative transfer equation in a channel. We demonstrate our theory with an example by comparison of an approximate solution with the exact solution. [ABSTRACT FROM AUTHOR]

Heart disease is a significant global health issue, contributing to high morbidity and mortality rates. Early and accurate heart disease prediction is crucial for effectively preventing and managing the condition. However, this remains a challenging task to achieve. This study proposes a machine learning model that leverages various preprocessing steps, hyperparameter optimization techniques, and ensemble learning algorithms to predict heart disease. To evaluate the performance of our model, we merged three datasets from Kaggle that have similar features, creating a comprehensive dataset for analysis. By employing the extra tree classifier, normalizing the data, utilizing grid search cross-validation (CV) for hyperparameter optimization, and splitting the dataset with an 80:20 ratio for training and testing, our proposed approach achieved an impressive accuracy of 98.15%. These findings demonstrated the potential of our model for accurately predicting the presence or absence of heart disease. Such accurate predictions could significantly aid in early prevention, detection, and treatment, ultimately reducing the mortality and morbidity associated with heart disease. [ABSTRACT FROM AUTHOR]

In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two applications on Riemann–Liouville fractional integrals and Atangana–Baleanu fractional integrals. [ABSTRACT FROM AUTHOR]

The goal of this paper is to obtain some tripled coincidence point results for generalized contraction mappings in the setting of JS-metric spaces endowed with a partial order. Furthermore, illustrative examples to support the theoretical results and the application are obtained. Finally, some theoretical results are applied to discuss the existence of a solution for a system of non-homogeneous and homogeneous integral equations as applications. [ABSTRACT FROM AUTHOR]

Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational inequality in mathematics is significantly aided by providing an important framework by fixed-point theory. The concept of fixed-point theory can be considered an inherent component of the VI. We consider a mixed variational inequality (MVI) a useful generalization of a classical variational inequality. The projection method is not applicable to solve MVI due to the involvement of the nonlinear term ϕ. MVI is equivalent to fixed-point problems and the resolvent equation techniques. This technique is commonly used in the research on the existence of a solution to the MVI. This paper uses a new self-adaptive method using step size to modify the fixed-point formulation for solving the MVI. We will also provide the convergence of the proposed scheme. Our output could be seen as a significant refinement of the previously known results for MVI. A numerical example is also provided for the implementation of the generated algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce Js;Ω-families of generalized pseudo-b-distances in b-gauge spaces (U; Qs;Ω). Moreover, by using these Js;Ω-families on U, we define the Js;Ω-sequential completeness and construct an F-type contraction T : U → U. Furthermore, we develop novel periodic and fixed point results for these mappings in the setting of b-gauge spaces using Js;Ω-families on U, which generalize and improve some of the results in the corresponding literature. The validity and importance of our theorems are shown through an application via an existence solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we have explored Noether symmetries for the Lagrangian corresponding to the Lemaitre-Tolman-Bondi (LTB) spacetime metric via a Rif tree approach. Instead of the frequently used method of directly integrating the Noether symmetry equations, a MAPLE algorithm is used to convert these equations to the reduced involutive form (Rif). The interesting feature of this algorithm is that it provides all possible metrics admitting different dimensional Noether symmetries. These metrics are given in the form of branches of a tree, known as a Rif tree. These metrics are used to solve the determining equations and the explicit form of symmetry vector fields are found, giving 4, 5, 6, 7, 8, 9, 11, and 17-dimensional Noether algebras. To add some physical implications, Einstein's field equations are used to find the stress-energy tensor for all the explicitly known metrics, and the parameters appearing in the metrics are used to find bounds for different energy conditions. [ABSTRACT FROM AUTHOR]

The article presents a systematic investigation of an extension of the developments concerning F-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of F-contractions to the case of non-linear (F, FH)-dynamic-iterative scheme for Branciari C' iric' type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determined. The paper also includes a tangible example and a graphical interpretation that displays the motivation for such investigations. The work is illustrated by providing an application of the proposed non-linear (F, FH)-dynamic-iterative scheme to the Liouville-Caputo fractional derivatives and fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of C*-algebra-valued b-asymmetric metric spaces and show several fixed point theorems that improve on a range of recent works in the literature. The C*-algebra-valued b-asymmetric metric space is illustrated with examples, as well as an application for determining the existence and uniqueness of a solution for a type of matrix equations and integral equation. [ABSTRACT FROM AUTHOR]

In this article, we present an orthogonal L -contraction mapping concepts and prove a fixed point theorem on orthogonal complete Branciari metric spaces. As an application, we apply our major results to solving integral equations. [ABSTRACT FROM AUTHOR]

In this article, we established a new version of generalized fractional Hadamard and Fejér--Hadamard type integral inequalities. A fractional integral operator (FIO) with a non-singular function (multi-index Bessel function) as its kernel and monotone increasing functions is utilized to obtain the new version of such fractional inequalities. Our derived results are a generalized form of several proven inequalities already existing in the literature. The proven inequalities are useful for studying the stability and control of corresponding fractional dynamic equations. [ABSTRACT FROM AUTHOR]

This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation with a nonlocal initial condition. We propose a fixed-point approach to investigate the existence, uniqueness, and Hyers-Ulam-Rassias stability of solutions. Results of this paper are based on nonstandard assumptions and hypothesis and provide a supplementary result concerning the regularity of solutions. We show and illustrate the wide validity field of our findings by an example of problem with nonlocal neutral pantograph equation, involving functional derivative and ψ -Caputo fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper, by introducing a convergence comparison property of a self-mapping, we establish some new fixed point theorems for Bianchini type, Reich type, and Dass-Gupta type dualistic contractions defined on a dualistic partial metric space. Our work generalizes and extends some well known fixed point results in the literature. We also provide examples which show the usefulness of these dualistic contractions. As an application of our findings, we demonstrate the existence of the solution of an elliptic boundary value problem. [ABSTRACT FROM AUTHOR]

In this manuscript, we establish results on the existence of common N-tupled fixed points using (CLR) property for two hybrid pair of mappings. We also study existence of a common solution for a system of N-integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we present a new notion which is called an extended Mb-metric space as a generalization of an Mb-metric space. We investigate some basic and topological properties of this new space. Furthermore, an extended Mb-metric space is a new generalization of an M-metric space and partial metric space. So it is important to study fixed-point theorems for non-M-metric (or non-partial metric) functions on an extended Mb-metric space. Also we generalize some known results in literature. [ABSTRACT FROM AUTHOR]

Fixed point theory can be extended to cover multidisciplinary area such computer science field. The proposed schema can be used for image authentication in order to ensure secure communication and detect any malicious modifications. In this paper, we generalize the M-metric space to the Mb-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Mb-metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce α-...-contractive self mapping in b-metric space and prove the existence of a fixed point for such mapping under some conditions. Some examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce α-Ψ-contractive self mapping in b-metric space and prove the existence of a fixed point for such mapping under some conditions. Some examples are given to illustrate the main results [ABSTRACT FROM AUTHOR]

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013), introduce the notion of complex valued b-metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self mappings on complex valued b-metric spaces. Some examples are given to illustrate the main results [ABSTRACT FROM AUTHOR]

We propose a convergence analysis of a new decomposition method to solve structured optimization problems. The proposed scheme is based on a class of modified Lagrangians combined with the allocation of resources decomposition algorithm. Under mild assumptions, we show that the method generates convergent primal-dual sequences. [ABSTRACT FROM AUTHOR]

The convergence problem of wavelet expansions is of the most recent interest in the theory of wavelets and it has been cleverly handled by various authors. In this paper, we establish a result on strong summability of wavelet expansions of periodic functions. [ABSTRACT FROM AUTHOR]

The aim of this work is to discuss the existence of solutions to the system of fractional variable order hybrid differential equations. For this reason, we establish coupled fixed point results in Banach spaces. [ABSTRACT FROM AUTHOR]

Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature. [ABSTRACT FROM AUTHOR]

In [Fixed Point Theory Appl., 2015 (2015):185], the authors introduced a new concept of modified contractive mappings, generalizing Ćirić, Chatterjea, Kannan, and Reich type contractions. They applied the condition (θ 4) (see page 3, Section 2 of the above paper). Later, in [Fixed Point Theory Appl., 2016 (2016):62], Jiang et al. claimed that the results in [Fixed Point Theory Appl., 2015 (2015):185] are not real generalizations. In this paper, by restricting the conditions of the control functions, we obtain a real generalization of the Banach contraction principle (BCP). At the end, we introduce a weakly JS-contractive condition generalizing the JS-contractive condition. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain a sufficient condition for a G-Cauchy sequence to be an M-Cauchy sequence in fuzzy metric spaces. Our main result provides a partial answer to the open question posed by V. Gregori and A. Sapena. For application, we give a new fuzzy version of the Banach fixed point theorem. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to construct q-Phillips operators generated by Dunkl generalization. We prove several results of Korovkin type and estimate the order of convergence in terms of several moduli of continuity. [ABSTRACT FROM AUTHOR]

In this manuscript, we propose a new class of Picard-Jungck operators for a pair of mappings on complete metric spaces by taking into account of the C G -simulation function. Also, some new results for the existence of such operators for a pair of self mappings in the setting of metric spaces are obtained. Some nontrivial examples are presented to show the usability of the results. [ABSTRACT FROM AUTHOR]

In this paper, we present the concept of Θ − (σ , ξ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results. [ABSTRACT FROM AUTHOR]