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 Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Linear System ◽  
Fixed Point Theorem ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Complete Controllability ◽  
Approximately Controllable ◽  
Sobolev Type Differential Equations

We discuss the approximate controllability of semilinear fractional Sobolev-type differential system under the assumption that the corresponding linear system is approximately controllable. Using Schauder fixed point theorem, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional Sobolev-type differential equations, are formulated and proved. We show that our result has no analogue for the concept of complete controllability. The results of the paper are generalization and continuation of the recent results on this issue.

scholarly journals Existence of nonoscillatory solutions tending to zero of fourth-order nonlinear neutral dynamic equations on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang-Cong Qiu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Neutral Dynamic Equations

AbstractIn this paper, a class of fourth-order nonlinear neutral dynamic equations on time scales is investigated. We obtain some sufficient conditions for the existence of nonoscillatory solutions tending to zero with some characteristics of the equations by Krasnoselskii’s fixed point theorem. Finally, two interesting examples are presented to show the significance of the results.

Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses

2019 ◽  
Vol 22 (2) ◽  
pp. 495-508 ◽  
Author(s):  
Jayanta Borah ◽  
Swaroop Nandan Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Fractional Order Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Abstract In this article, we establish a set of sufficient conditions for the existence of mild solution of a class of fractional differential equations with not instantaneous impulses. The results are obtained by using Banach fixed point theorem and Krasnoselskii’s fixed point theorem. An example is presented for validation of result.

scholarly journals Approximate Controllability of Neutral Measure Evolution Equations with Nonlocal Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Lina Ma ◽  
Haibo Gu ◽  
Yiru Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Sufficient Conditions

In this paper, we consider a kind of neutral measure evolution equations with nonlocal conditions. By using semigroup theory and fixed point theorem, we can obtain sufficient conditions for the controllability results of such equations. Finally, an example is given to verify the reliability of the results.

scholarly journals Second order evolution equations with nonlocal conditions

2017 ◽  
Vol 50 (1) ◽  
pp. 309-319 ◽  
Author(s):  
Mouffak Benchohra ◽  
Juan J. Nieto ◽  
Noreddine Rezoug
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Hausdorff Measure ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Fréchet Spaces

Abstract In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.

scholarly journals Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

2017 ◽  
Vol 4 (1) ◽  
pp. 1-15
Author(s):  
Machindra B. Dhakne ◽  
Poonam S. Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Fractional Power Of Operators

Abstract In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

scholarly journals Existence of Positive Periodic Solutions for a Class ofn-Species Competition Systems with Impulses

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Peilian Guo ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Species Competition ◽  
Positive Periodic Solutions ◽  
The Fixed Point Theorem

By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class ofn-species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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.

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