scholarly journals Continuous dependence for NLS in fractional order spaces

2011 ◽  
Vol 28 (1) ◽  
pp. 135-147 ◽  
Author(s):  
Thierry Cazenave ◽  
Daoyuan Fang ◽  
Zheng Han
Keyword(s):  
Fractional Order ◽  
Continuous Dependence

scholarly journals Coupled system of a fractional order differential equations with weighted initial conditions

2019 ◽  
Vol 17 (1) ◽  
pp. 1737-1749
Author(s):  
Ahmed M. A. El-Sayed ◽  
Sheren A. Abd El-Salam
Keyword(s):  
Fractional Order ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Coupled System ◽  
Cauchy Type ◽  
Type Problem ◽  
Integrable Solution ◽  
Fractional Order Differential Equations ◽  
Cauchy Type Problem ◽  
Uniqueness Of The Solution

Abstract Here, a coupled system of nonlinear weighted Cauchy-type problem of a diffre-integral equations of fractional order will be considered. We study the existence of at least one integrable solution of this system by using Schauder fixed point Theorem. The continuous dependence of the uniqueness of the solution is proved.

scholarly journals Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 331 ◽  
Author(s):  
Yu Chen ◽  
JinRong Wang
Keyword(s):  
Fractional Order ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Impulsive Differential Equations ◽  
Junction Points ◽  
Random Impulse ◽  
Continuous Dependence Results ◽  
Theoretical Results ◽  
Continuous Dependence Of Solutions

This paper gives continuous dependence results for solutions of integer and fractional order, non-instantaneous impulsive differential equations with random impulse and junction points. The notion of the continuous dependence of solutions of these equations on the initial point is introduced. We prove some sufficient conditions that ensure the solutions to perturbed problems have a continuous dependence. Finally, we use numerical examples to demonstrate the obtained theoretical results.

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