scholarly journals Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for α-Admissible Fψ1,ψ2−Contractions in M−Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Erdal Karapinar ◽  
Shimaa I. Moustafa ◽  
Ayman Shehata ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Admissible Mapping ◽  
Linear Perturbations ◽  
Uniqueness Of A Solution ◽  
Hybrid Differential Equations

In this paper, we investigate the existence of a unique coupled fixed point for α−admissible mapping which is of Fψ1,ψ2−contraction in the context of M−metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Investigating a Coupled Hybrid System of Nonlinear Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wiyada Kumam ◽  
Mian Bahadur Zada ◽  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Point Boundary ◽  
Coupled Fixed Point Theorem ◽  
Fractional Differential

We study sufficient conditions for existence of solutions to the coupled systems of higher order hybrid fractional differential equations with three-point boundary conditions. For this motive, we apply the coupled fixed point theorem of Krasnoselskii type to form adequate conditions for existence of solutions to the proposed system. We finish the paper with suitable illustrative example.

scholarly journals Endpoints of multi-valued weakly contraction in complete metric spaces endowed with graphs

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4319-4329 ◽  
Author(s):  
Jukrapong Tiammee ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered

In this paper, we introduce a new concept of weak G-contraction for multi-valued mappings on a metric space endowed with a directed graph. Endpoint theorem of this mapping is established under some sufficient conditions in a complete metric space endowed with a directed graph. Our main results extend and generalize those fixed point in partially ordered metric spaces. Some examples supporting our main results are also given. Moreover, we apply our main results to obtain some coupled fixed point results in the context of complete metric spaces endowed with a directed graph which are more general than those in partially ordered metric spaces.

scholarly journals Existence and uniqueness of the solutions of some classes of integral equations C*-algebra-valued b-metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 726-742
Author(s):  
Esad Jakupović ◽  
Hashem Masiha ◽  
Zoran Mitrović ◽  
Seyede Razavi ◽  
Reza Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Point Theory ◽  
C Algebra ◽  
Coupled Fixed Points

Introduction/purpose: The aim of the paper is to establish some coupled fixed point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. Methods: The method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. Results: New results were obtained on coupled fixed points in C*-algebra-valued b-metric space. Conclusion: The obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations.

scholarly journals Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Aziz Khan ◽  
Kamal Shah ◽  
Yongjin Li ◽  
Tahir Saeed Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Generalized Metric Space ◽  
Ulam Stability ◽  
Fractional Differential ◽  
Necessary And Sufficient

We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.

scholarly journals Coupled Fixed Point Results in Banach Spaces with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2283
Author(s):  
Mian Bahadur Zada ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Variable Order ◽  
Hybrid Differential Equations

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.

scholarly journals Different types of Hyers-Ulam-Rassias stabilities for a class of integro-differential equations

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5379-5390 ◽  
Author(s):  
L.P. Castro ◽  
A.M. Simões
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Volterra Type ◽  
Different Types ◽  
Infinite Intervals ◽  
Type Of Stability ◽  
Rassias Stability

We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of semi-Hyers-Ulam-Rassias stability, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.

scholarly journals Hybrid Coupled Fixed Point Theorems in Metric Spaces with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Muhammad Shoaib ◽  
Muhammad Sarwar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Coupled System ◽  
Matrix Equations ◽  
Common Coupled Fixed Point ◽  
Nonlinear Matrix ◽  
Two Hybrid ◽  
Coupled Coincidence

In this manuscript, using CLR property, coupled coincidence and common coupled fixed point results for two-hybrid pairs satisfying (F,φ)- contraction are demonstrated. Using the established results existence of solution to the coupled system of functional and nonlinear matrix equations is also discussed. We provide examples where the main theorem is applicable but most current relevant results in literature fail to have a common coupled fixed point.

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