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View article: New α-ɛ-Suzuki-Type Contraction Mapping Methods on Fractional Differential and Integral Equations
New α-ɛ-Suzuki-Type Contraction Mapping Methods on Fractional Differential and Integral Equations Open
This paper introduces novel formulations in the framework of α−E-contractions within the context of admissible mappings. We establish new fixed point theorems for α−E-Suzuki-type contractions, thereby generalizing and extending the foundat…
View article: Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations
Novel Fixed Point Results in Rectangular Gb-Metric Spaces and Some Applications on Fractional Differential Equations Open
In this work, we prove some fixed point theorems in rectangular Gb-metric space, which is the generalization of rectangular metric space and Gb-metric space. Moreover, we give some examples to support our theoretical findings. Finally, usi…
View article: Mathematical SEIR Model of the Lumpy Skin Disease Using Caputo-Fabrizio Fractional-Order
Mathematical SEIR Model of the Lumpy Skin Disease Using Caputo-Fabrizio Fractional-Order Open
Of the seventeen sustainable development goals given out by the United Nations, the third focuses on good health and well-being, while the 15th focuses on life on land. This research aims to study an integral model of Lumpy Skin Disease to…
View article: Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique
Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique Open
The primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditi…
View article: A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method
A Novel Approach for Solving Fractional Differential Equations via a Multistage Telescoping Decomposition Method Open
This study presents a novel algorithm for solving nonlinear fractional initial value problems, utilizing a multistage telescoping decomposition method (FTDM). By combining the MFTDM with the Elzaki transform, this method significantly impr…
View article: Mathematical Model of the Waste Plastic Management via ABC Fractional Order Derivative
Mathematical Model of the Waste Plastic Management via ABC Fractional Order Derivative Open
Plastic waste can be broadly classified as recyclable and nonrecyclable wastes. The United Nations has set 17 goals of which Goal 14 refers to “Life below Water.” If plastic waste is not properly managed, it can pose a health hazard, inclu…
View article: Existence results for periodic fractional differential equation involving deformable derivative
Existence results for periodic fractional differential equation involving deformable derivative Open
In this paper, a differential equation problem with periodic boundary value conditions involving deformable derivative is considered. We demonstrate the existence of solution to this problem by applying the solution-tube method and Schaude…
View article: Digital h-Fibrations and Some New Results on Digital Fibrations
Digital h-Fibrations and Some New Results on Digital Fibrations Open
In this work, the notion of digital fiber homotopy is defined and its properties are given. We present some new results on digital fibrations. Moreover, we introduce digital h-fibrations. We prove some of the properties of these digital h-…
View article: A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques
A Numerical Scheme and Application to the Fractional Integro-Differential Equation Using Fixed-Point Techniques Open
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 …
View article: Existence and uniqueness results on coupled Caputo-Hadamard fractional differential equations in a bounded domain
Existence and uniqueness results on coupled Caputo-Hadamard fractional differential equations in a bounded domain Open
In this article, we study the existence and uniqueness of solutions for a boundary value problem of coupled system of Caputo-Hadamard fractional differential equations in a bounded domain. Banach contraction mapping principle and Schaefer?…
View article: On elliptic valued b-metric spaces and some new fixed point results with an application
On elliptic valued b-metric spaces and some new fixed point results with an application Open
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 t…
View article: Fixed point results via O-Fϱ contraction and applications to Fredholm and integro-differential equations
Fixed point results via O-Fϱ contraction and applications to Fredholm and integro-differential equations Open
In this article, we introduce the new concept of an O-F? contraction on O-controlled O-b-Branciari metric type spaces. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficia…
View article: Boyd-Wong type contractions in generalized parametric bipolar metric space
Boyd-Wong type contractions in generalized parametric bipolar metric space Open
In this manuscript, we introduce a new notion of generalized parametric bipolar metric space as a generalization of generalized parametric space and bipolar metric space. We also introduce Boyd-Wong type contractions for covariant and cont…
View article: Hopf structures on closure spaces
Hopf structures on closure spaces Open
This study extends algebraic perspectives to non-topological closure spaces by introducing Hopf structures. We define closure Hopf spaces and groups, investigate their properties, and explore homotopy theory within this framework. Contrava…
View article: Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces
Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces Open
In this manuscript, we establish some fixed-point theorems without continuity by using the triangular property on a fuzzy bipolar b-metric space as a generalized version and expansion of the well-known results. We also provide some example…
View article: Orthogonal neutrosophic 2-metric spaces
Orthogonal neutrosophic 2-metric spaces Open
In this study, we introduce the notion of an orthogonal neutrosophic 2-metric space and prove the common fixed-point theorem on an orthogonal neutrosophic 2-metric space. From the obtained results, we give an example to support our results.
View article: The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations
The Study of Bicomplex-Valued Controlled Metric Spaces with Applications to Fractional Differential Equations Open
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 applicati…
View article: Controlled S-Metric-Type Spaces and Applications to Fractional Integrals
Controlled S-Metric-Type Spaces and Applications to Fractional Integrals Open
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 …
View article: Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces
Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces Open
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 applica…
View article: Fixed Point Results in C★-Algebra-Valued Partial b-Metric Spaces with Related Application
Fixed Point Results in C★-Algebra-Valued Partial b-Metric Spaces with Related Application Open
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 …
View article: A Study on Fixed-Point Techniques under the α-ϝ-Convex Contraction with an Application
A Study on Fixed-Point Techniques under the α-ϝ-Convex Contraction with an Application Open
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 r…
View article: New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications
New Fixed Point Results in Orthogonal B-Metric Spaces with Related Applications Open
In this article, we present the concept of orthogonal α-almost Istra˘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…
View article: Solution of Fredholm Integral Equation via Common Fixed Point Theorem on Bicomplex Valued B-Metric Space
Solution of Fredholm Integral Equation via Common Fixed Point Theorem on Bicomplex Valued B-Metric Space Open
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 bicomp…
View article: Solution of an integral equation in G-metric spaces
Solution of an integral equation in G-metric spaces Open
In this paper, we prove a fixed point result in G-metric spaces satisfying generalized contractive condition with new auxiliary functions, which generalize the result of Bhardwaj and Kumar. The motivation of this paper is to observe the so…
View article: New results on fractional relaxation integro differential equations with impulsive conditions
New results on fractional relaxation integro differential equations with impulsive conditions Open
The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation impulsive integro-differential equations with boundary conditions. Some results are established by using the Banach contraction…
View article: On a coupled system of generalized hybrid pantograph equations involving fractional deformable derivatives
On a coupled system of generalized hybrid pantograph equations involving fractional deformable derivatives Open
The goal of this work is to study the existence of a unique solution and the Ulam-Hyers stability of a coupled system of generalized hybrid pantograph equations with fractional deformable derivatives. Our main tool is Banach's contraction …
View article: Boundary value problems of higher order fractional integro-differential equations involving Gronwall's inequality in Banach spaces
Boundary value problems of higher order fractional integro-differential equations involving Gronwall's inequality in Banach spaces Open
Using the Caputo derivative of order q ∈ (α -1, α), we examine boundary value problems for fractional integro-differential equations in Banach spaces.Using an a priori estimate technique, the Holder's inequality, a suitable singular Gronwa…
View article: Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces
Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces Open
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 applic…
View article: Solving a Boundary Value Problem via Fixed-Point Theorem on ®-Metric Space
Solving a Boundary Value Problem via Fixed-Point Theorem on ®-Metric Space Open
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 giv…