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. 

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 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 Bottom-Up derivatives of tree expressions

2021 ◽  
Vol 55 ◽  
pp. 4
Author(s):  
Samira Attou ◽  
Ludovic Mignot ◽  
Djelloul Ziadi
Keyword(s):  
Fixed Point ◽  
Tree Automaton ◽  
Bottom Up ◽  
Regular Tree ◽  
Partial Derivatives ◽  
New Family ◽  
Derivatives Of

In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended regular tree expressions (using negation or intersection operators), and we show how to compute a Brzozowski-like inductive tree automaton; the fixed point of this construction, when it exists, is the derivative tree automaton. Such a deterministic tree automaton can be used to solve the membership test efficiently: the whole structure is not necessarily computed, and the derivative computations can be performed in parallel. We also show how to solve the membership test using our (Bottom-Up) partial derivatives, without computing an automaton.

scholarly journals Exact Controllability for Hilfer Fractional Differential Inclusions Involving Nonlocal Initial Conditions

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Du ◽  
Wei Jiang ◽  
Denghao Pang ◽  
Azmat Ullah Khan Niazi
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Fractional Differential Inclusions ◽  
Nonlocal Initial Conditions ◽  
Fractional Differential System ◽  
Fractional Differential

The exact controllability results for Hilfer fractional differential inclusions involving nonlocal initial conditions are presented and proved. By means of the multivalued analysis, measure of noncompactness method, fractional calculus combined with the generalized Mo¨nch fixed point theorem, we derive some sufficient conditions to ensure the controllability for the nonlocal Hilfer fractional differential system. The results are new and generalize the existing results. Finally, we talk about an example to interpret the applications of our abstract results.

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 ON THE CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

2019 ◽  
Vol 6 (1) ◽  
pp. 17-22
Author(s):  
Valliammal N ◽  
Ravichandran C
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Mönch Fixed Point Theorem

In this paper, we established the some sufficient conditions for controllability of impulsive functional integrodifferential equations with nonlocal conditions by using the measure of noncompactness and Monch fixed point theorem.

scholarly journals On the controllability of Hilfer-Katugampola fractional differential equations

2020 ◽  
Vol 24 (2) ◽  
pp. 195-204
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Fractional Differential

By employing Kuratowski's measure of noncompactness together with Sadovskii's fixed point theorem, sufficient conditions for controllability results of Hilfer-Katugampola fractional differential equations in Banach spaces are derived.

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