Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

2018 ◽  
Vol 21 (2) ◽  
pp. 725-748 ◽  
Author(s):  
Zuomao Yan ◽  
Xiumei Jia
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Optimal Mild Solutions

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

On optimal mild solutions of non-homogeneous differential equations in Banach spaces

1979 ◽  
Vol 84 (3-4) ◽  
pp. 273-277 ◽  
Author(s):  
S. Zaidman
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Real Line ◽  
Infinitesimal Generator ◽  
Existence Result ◽  
Mild Solutions ◽  
Optimal Solutions ◽  
Uniformly Convex ◽  
Optimal Mild Solutions

SynopsisConsider mild solutions on the real line of non-homogeneous differential equations in a Banach space: u′(t) = Au(t) + f(t), where A is the infinitesimal generator of a C0-semigroup.We prove an existence result for optimal solutions (as defined in the text) in reflexive spaces and an uniqueness fact in uniformly convex B-spaces.

scholarly journals The Kneser property for abstract retarded functional differential equations with infinite delay

2003 ◽  
Vol 2003 (26) ◽  
pp. 1645-1661 ◽  
Author(s):  
Hernán R. Henríquez
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
First Order ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

We establish existence of mild solutions for a class of semilinear first-order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.

scholarly journals Well posedness results for higher-order neutral stochastic differential equations driven by Poisson jumps and Rosenblatt process

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 353-365
Author(s):  
K. Ramkumar ◽  
K. Ravikumar ◽  
A. Anguraj ◽  
Hamdy Ahmed
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Successive Approximation Method ◽  
Poisson Jumps ◽  
Rosenblatt Process

In this article, we investigate the existence, uniqueness and stability of mild solutions for a class of higher-order nonautonomous neutral stochastic differential equations (NSDEs) with infinite delay driven by Poisson jumps and Rosenblatt process in Hilbert space. More precisely, using semigroup theory and successive approximation method, we establish a set of sufficient conditions for obtained the required result. Further, the result is deduced to study the higher-order autonomous system. Finally, examples are provided to demonstrate the obtain results.

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