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In this paper, we introduce the notion of orthogonal α –F–convex contraction mapping and prove some fixed-point theorems for self-mapping in orthogonal complete metric spaces. The proven results generalize and extend some of the well-known results in the literature. Following the derivation of these fixed-point results, we propose a solution for the fractional integro-differential equation, utilizing the fixed-point technique within the context of orthogonal complete metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the b-triangular property in fuzzy b-metric space. Furthermore, we give some new fixed point results in fuzzy b-metric space for non-continuous mappings. Our results generalize and expand some results from the related literature. Two applications of our results, to solving Fredholm integral equation and in dynamic programming, are also given. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of neutrosophic pentagonal metric space. We prove several interesting results for some classes contraction mappings and prove some fixed point theorems in neutrosophic pentagonal metric space. Finally, we prove the uniqueness and existence of the integral equation and fractional differential equation to support our main result. [ABSTRACT FROM AUTHOR]

In the present paper, we prove common fixed point theorems under different contractive mappings on C ★ -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of bicomplex-valued controlled metric spaces and prove fixed point theorems. Our results mainly focus on generalizing and expanding some recently established results. Finally, we explain an application of our main result to a certain type of fractional differential equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of fuzzy-controlled bipolar metric space and prove some fixed-point theorems in this space. Our results generalize and expand some of the literature's well-known results. We also provide some applications of our main results to integral equations. [ABSTRACT FROM AUTHOR]

Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation. [ABSTRACT FROM AUTHOR]

In this article, we establish fixed point results by defining the concept of F -Khan contraction of an orthogonal set by modifying the symmetry of usual contractive conditions. We also provide illustrative examples to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with numerical simulation. [ABSTRACT FROM AUTHOR]

In this manuscript, we prove some fixed point theorems on C-algebra-valued partial b-metric spaces by using generalized contraction. We give support and suitable examples of our main results. Moreover, we present a generative application of the main results. [ABSTRACT FROM AUTHOR]

The notion of symmetry is the main property of a metric function. The area of fixed point theory has a suitable structure for symmetry in mathematics. The goal of this paper is to find fixed point and common fixed point results in a bicomplex valued b-metric space for mixed type rational contractions with control functions. Some well-known literature findings were generalized in our main findings. We provide an example to strengthen and validate our main results. As an example, in the context of bicomplex-valued b-metric space, we develop fixed point and common fixed point results for the rational contraction mapping. [ABSTRACT FROM AUTHOR]

In this article, we present the concept of orthogonal α -almost Istr a ˘ tescu contraction of types D and D * and prove some fixed point theorems on orthogonal b-metric spaces. We also provide an illustrative example to support our theorems. As an application, we establish the existence and uniqueness of the solution of the fractional differential equation and the solution of the integral equation using Elzaki transform. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of the solution for the spring-mass system via an integral equation with a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we consider several classes of mappings related to the class of α - ϝ -contraction mappings by introducing a convexity condition and establish some fixed-point theorems for such mappings in complete metric spaces. The present result extends and generalizes the well-known results of α -admissible and convex contraction mapping and many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results. Finally, we derive the existence and uniqueness of a solution to an integral equation to support our main result and give a numerical example to validate the application of our obtained results. [ABSTRACT FROM AUTHOR]

Our paper is devoted to describing a new way of generalized convex contraction of type-2 in the framework of b-metric spaces and 2-metric spaces. First, the concept of a new generalized convex contraction on b-metric spaces and 2-metric spaces is introduced, and fixed point theorem is extended to these spaces. Some examples supporting our main results are also presented. Finally, we apply our main result to approximating the solution of the Fredholm integral equation. [ABSTRACT FROM AUTHOR]

In this present study, we propose the concept of tricomplex-controlled metric spaces as a generalization of both controlled metric-type spaces and tricomplex metric-type spaces. In this work, we establish fixed point results using Banach, Kannan and Fisher-type contractions supported with nontrivial examples in the setting of the proposed space. We apply the derived result to find the analytical solution of an integral equation using the fixed point technique under the same metric. [ABSTRACT FROM AUTHOR]

In this paper, we prove the fixed-point theorem for rational contractive mapping on ®-metric space. Additionally, an Euclidean metric space with a binary relation example and an application to the first-order boundary value problem are given. Moreover, the obtained results generalize and extend some of the well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove fixed point theorem via orthogonal Geraghty type α -admissible contraction map in an orthogonal complete Branciari b-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of neutrosophic rectangular triple-controlled metric space, relaxing the symmetry requirement of neutrosophic metric spaces, by replacing triangular inequalities with rectangular inequalities, and prove fixed point theorems. We have derived several interesting results for contraction mappings supplemented with non-trivial examples. The derived results have been applied to prove the existence of a unique analytical solution as well as a closed form of the unique solution to the integral equation. [ABSTRACT FROM AUTHOR]

In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of the literature's well-known results. We also explore some of the applications to our key results. [ABSTRACT FROM AUTHOR]

The idea of symmetry is a built-in feature of the metric function. In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via orthogonal triangular α-orbital admissible mapping in the context of orthogonal complete Branciari metric spaces endowed with a transitive binary relation. Our results generalize and extend some pioneering results in the literature. Furthermore, the existence criteria of the solutions to fractional integro-differential equations are established to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

Metric fixed point theory has vast applications in various domain areas, as it helps in finding analytical solutions under various contractive conditions, including non-linear integral-type contractions. In our present work, we have established fixed point results in the setting of complex valued partial metric space. Our results extend the results proven in literature. Using our main result, we have provided an application to find the solution to the Urysohn-type integral equation. [ABSTRACT FROM AUTHOR]

In this paper, motivated by the recent result of Sezen, we introduce the notion of fuzzy triple controlled bipolar metric space and prove some fixed point results in this framework. Our results generalize and extend some of the well-known results from the literature. We also explore some of the applications of our key results to integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of bicomplex partial metric space and prove some common fixed point theorems. The presented results generalize and expand some of the literature's well-known results. An example and application on bicomplex partial metric space is given. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed-point theorems on complex partial metric space. The presented results generalize and expand some of the well-known results in the literature. We also explore some of the applications of our key results. [ABSTRACT FROM AUTHOR]