scholarly journals Existence and uniqueness of solutions for a system of impulsive differential equations on the half-line

2017 ◽  
Vol 2017 (1) ◽  
pp. 1-16 ◽  
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equations ◽  
Half Line ◽  
Uniqueness Of Solutions

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR STOCHASTIC IMPULSIVE DIFFERENTIAL EQUATIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 375-383 ◽  
Author(s):  
LIJUAN SHEN ◽  
JITAO SUN
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Uniqueness Of Solutions ◽  
Special Requirement ◽  
Impulsive Function

This paper is concerned with the existence and uniqueness of solutions for stochastic impulsive differential equations. Some sufficient conditions are obtained by using the notion of measure of noncompactness and the Leray–Schauder type fixed theorem. Since the conditions do not need special requirement of the impulsive function, the results we obtained is more reflexible. An example will illustrate the effectiveness.

When do fractional differential equations have solutions that are bounded by the Mittag--Leffler function ?

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Christopher C. Tisdell
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Half Line ◽  
Growth Behaviour ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
Fixed Point Methods

AbstractWhen do fractional differential equations have solutions on the half line that are bounded by the Mittag-Leffler function? This work answers the above question through fixed-point methods, providing a deeper understanding of the long term growth behaviour of solutions, in addition to advancing our knowledge on the existence and uniqueness of solutions. A YouTube video by the Author that complements this work can be found at http://tinyurl.com/FDE-ML.

scholarly journals On coupled systems of fractional impulsive differential equations by using a new Caputo-Fabrizio fractional derivative

2020 ◽  
Vol 24 (2) ◽  
pp. 1-19
Author(s):  
Ahmed Boudaoui ◽  
Abdeldjalil Slama
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Impulsive Differential Equations ◽  
Coupled System ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Generalized Metric Spaces ◽  
Solution Sets ◽  
Fixed Point Approach

In this paper, we investigate the existence and uniqueness of solutions for coupled system of Caputo-Fabrizio fractional impulsive differential equations using the fixed point approach in generalized metric spaces. The compactness of solution sets of the system is also investigated. An example is provided to illustrate the developed theory.

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