Existence of coupled fixed point via measure of noncompactness

2021 ◽  
Author(s):  
K. Mebarki ◽  
A. Boudaoui ◽  
W. Shatanawi
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Coupled Fixed Point

scholarly journals Solvability of fractional dynamic systems utilizing measure of noncompactness

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Rabha W. Ibrahim ◽  
Reza Arab ◽  
Mohsen Rabbani
Keyword(s):  
Fixed Point ◽  
Dynamic Systems ◽  
Measure Of Noncompactness ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Fractional Dynamics ◽  
New Family ◽  
Growth System ◽  
Derivatives Of

Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in Rn for fractional dynamic systems. To accomplish it, we introduce first the concept of (F, ψ)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large. 

scholarly journals Application of measure of noncompactness for the system of functional integral equations

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3063-3073 ◽  
Author(s):  
Reza Arab
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Darbo Fixed Point Theorem ◽  
Functional Integral Equations

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banch space via the measure of non-compactness, which generalize the result of Aghajani et al.[6]. Our results generalize, extend, and unify several well-known comparable results in the literature. As an application, we study the existence of solutions for the system of integral equations.

scholarly journals An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 879-886 ◽  
Author(s):  
A. Samadi ◽  
M.B. Ghaemi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Coupled Fixed Point ◽  
Coupled Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

In this paper, an extension of Darbo fixed point theorem is introduced. By applying our extension, we obtain a coupled fixed point theorem and a solution for an integral equation. The proofs of our results are based on the technique of measure of noncompactness.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

scholarly journals Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sina Etemad ◽  
Mohammed Said Souid ◽  
Benoumran Telli ◽  
Mohammed K. A. Kaabar ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Research Work ◽  
Neutral System ◽  
Fractional Differential Inclusions ◽  
Kuratowski Measure Of Noncompactness ◽  
Fractional Differential

AbstractA class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

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 An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

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