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This paper examines the analysis of some rational-type contractions within the context of extended b-metric spaces, establishes a theoretical foundation for rational-type contractions and demonstrates their application in Volterra integral inclusions and Urysohn integral equations. Some examples are provided for the authenticity of the findings.

In this paper, we present fixed point theorem for mappings defined on b-metric spaces, which satisfies extended quasi-contractive inequality with nonlinear comparison function. Our result generalizes and improves several recent results from fixed point theory.

In this paper, we introduce the concept of the rectangular M-metric spaces, along with its topology and we prove some fixed-point theorems under different contraction principles with various techniques. The obtained results generalize some classical fixed-point results such as the Banach’s contraction principle, the Kannan’s fixed-point theorem and the Chatterjea’s fixed-point theorem. Also we give an application to the fixed-circle problem.

This study examines marangoni convection in blood-based carbon nanotubes nanofluid's stagnation point flow over a time-dependent stretching surface. This study is inspired by the emerging importance of nanofluids in a variety of scientific and technical fields due to their unique and varied uses and effective thermal activities. Some examples of potential applications of these fluids include cancer treatment, magnetic refrigeration, drug delivery, and magnetic resonance imaging. Two types of nanoparticles are considered name is single wall carbon nanotube and multi wall carbon nanotube blood is takin as base fluid. Nonlinear partial differential equations are used to simulate the specified flow issue using momentum and energy conservation principles. Using a similarity transformation, the resultant is transformed into nonlinear with reduced dimensions.  The relations for velocity profile and temperature distribution are calculated from the developed nonlinear ordinary differential equation by using an approximate analytical technique called the homotopy asymptotic method. Subsequently, these equations are implemented and executed within Mathematica software. The investigation focuses on significant outcomes such as momentum filed, energy filed, Skin friction coefficients, and Nusselt number. Graphs are used to interpret the effects of several factors, including the Marangoni parameter, nanoparticle volume friction, stretching parameter, slip parameter, and Prandtl number. The behavior of Nusselt's number and skin friction coefficient was also checked with the help of graphs and tables. The convergence of the solutions is checked with the help of auxiliary functions as well.

We present iterative approximation results of an iterative scheme for finding common fixed points of edge-preserving quasi-nonexpansive self-maps in Hilbert spaces along with directed graph. We obtain weak as well as strong convergence of our scheme under various assumptions. That is, we impose several possible mild conditions on the domain, on the mapping, or on the parameters involved in our scheme to prove convergence results. We support numerically our main outcome by giving an example. Eventually, an application is provided for solving a variational inequality problem. Our result are new/generalized some recently announced results of the literature.

In this paper, a numerical technique is developed for the solution of multi-term fractional differential equations (FDEs) upto fourth order by using Haar collocation method (HCM). In Caputo sense, the fractional derivative is defined. The integral involved in the equations is calculated by the method of Lepik. The HCM converts the given multi-term FDEs into a system of linear equations. The convergence of the proposed method HCM is checked on some problems. Mean square root and maximum absolute errors are calculated for different numbers of collocation points(CPs), which are recorded in tables. The exact and approximate solution comparison is also given in figures. The time taken by CPU for numerical results is also given in the tables.

The purpose of this article is to introduce locally α-ζ-multivalued contraction and rational Ćirić type α-ζ-multivalued contraction in the context of F-metric spaces and prove some endpoint results. We provide a nontrivial example to show the authenticity of our main result. Our results generalize some well-known results of literature. We also present some endpoint results in both graphic F-metric spaces and ordered F-metric spaces. As an application of our main result, we investigate the solution of an integral equation.

In this manuscript, common fixed point results for set-valued mapping under generalized ψ,ϕ1 and ψ,ϕ2 weak contraction without using Hausdorff metric are studied endowing with a graph. To demonstrate the authenticity of the established result, a suitable example and application to integral inclusion are also discussed.

In this paper, a new class of functions denoted by Ψν is introduced which we use to prove new interesting fixed point results in controlled metric type spaces. Also, we present examples to illustrate our work.

In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution. Also, we give an example to illustrate our work.

In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on higher degree polynomial equations.

In this work, we extend and complement some results in view of general and wider structures, such as b−metric spaces. By considering existing classes of Ζ−contractions and Ψ−simulating functions with a solid impact in database results of fixed point theory, we introduce a new general class of simulating functions, called as Ψ−s simulation functions, and also types of κψ−s− contractions in a more general framework. This approach covers, extends, and unifies several published works in the early and late literature.

In this article, we discuss a new version of metric fixed point theory. The application of this newly introduced concept is to find some fixed point results where many well-known results in literature cannot be applied. We give some examples to illustrate the given concepts and obtained results.

In this paper, we present new fixed-circle theorems for self-mappings on an S-metric space using some Wardowski type contractions, ψ-contractive, and weakly ψ-contractive self-mappings. The common property in all of the obtained theorems for Wardowski type contractions is that the self-mapping fixes both the circle and the disc with the center x0 and the radius r.