scholarly journals Controllability of Differential Systems with the General Conformable Derivative

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ferrag Azouz ◽  
Djalal Boucenna ◽  
Abdellatif Ben Makhlouf ◽  
Lassaad Mchiri ◽  
Abbes Benchaabane
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Necessary Conditions ◽  
Order System ◽  
Complete Controllability ◽  
Conformable Derivative ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Controllability Result

In this paper, the controllability of differential systems with the general conformable derivative is studied. By elaborating the rank criterion and the conformable Gram criterion, sufficient and necessary conditions to investigate that a linear general conformable system is null completely controllable are given. We obtain a full generalization to the general conformable fractional-order system case. In addition, Krasnoselskii’s fixed point theorem to obtain a complete controllability result for a semilinear general conformable system is applied.

scholarly journals Controllability of conformable differential systems

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Xiaowen Wang ◽  
JinRong Wang ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Necessary Conditions ◽  
Complete Controllability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Numerical Examples ◽  
Controllability Of Systems ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results ◽  
Controllability Result

This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.  

scholarly journals First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Dumitru Baleanu ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
First Order ◽  
Impulsive Differential Systems ◽  
Sufficient And Necessary Conditions

AbstractIn this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results.

scholarly journals Nonoscillatory solutions to fourth-order neutral dynamic equations on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yang-Cong Qiu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Fourth Order ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, we present some sufficient conditions and necessary conditions for the existence of nonoscillatory solutions to a class of fourth-order nonlinear neutral dynamic equations on time scales by employing Banach spaces and Krasnoselskii’s fixed point theorem. Two examples are given to illustrate the applications of the results.

scholarly journals Complete Controllability of Impulsive Stochastic Integrodifferential Systems in Hilbert Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xisheng Dai ◽  
Feng Yang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Complete Controllability ◽  
Differential Systems ◽  
Stochastic Wave Equation

This paper concerns the complete controllability of the impulsive stochastic integrodifferential systems in Hilbert space. Based on the semigroup theory and Burkholder-Davis-Gundy's inequality, sufficient conditions of the complete controllability for impulsive stochastic integro-differential systems are established by using the Banach fixed point theorem. An example for the stochastic wave equation with impulsive effects is presented to illustrate the utility of the proposed result.

scholarly journals Complete Controllability for Fractional Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xia Yang ◽  
Haibo Gu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Nonlocal Condition ◽  
Sufficient Conditions ◽  
General Concept ◽  
Complete Controllability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Evolution Equation

The paper is concerned with the complete controllability of fractional evolution equation with nonlocal condition by using a more general concept for mild solution. By contraction fixed point theorem and Krasnoselskii's fixed point theorem, we obtain some sufficient conditions to ensure the complete controllability. Our obtained results are more general to known results.

scholarly journals Complete Controllability of Fractional Neutral Differential Systems in Abstract Space

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Fang Wang ◽  
Zhen-hai Liu ◽  
Jing Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Power ◽  
Complete Controllability ◽  
Abstract Space ◽  
Differential Systems ◽  
Characteristic Solution Operators ◽  
Sadovskii Fixed Point Theorem ◽  
Fractional Power Of Operators

By using fractional power of operators and Sadovskii fixed point theorem, we study the complete controllability of fractional neutral differential systems in abstract space without involving the compactness of characteristic solution operators introduced by us.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

scholarly journals Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Naveed Ahmad ◽  
Zeeshan Ali ◽  
Kamal Shah ◽  
Akbar Zada ◽  
Ghaus ur Rahman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Dynamical Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

scholarly journals Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

2018 ◽  
Vol 36 (2) ◽  
pp. 185
Author(s):  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scale ◽  
Variable Coefficients ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations ◽  
Compact Map

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

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