Periodic Mild Solutions of Infinite Delay not Instantaneous Impulsive Evolution Inclusions

2021 ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Gaston N’Guérékata
Keyword(s):  
Infinite Delay ◽  
Mild Solutions ◽  
Evolution Inclusions

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.

Semilinear fractional order integro-differential inclusions with infinite delay

2018 ◽  
Vol 25 (3) ◽  
pp. 317-327 ◽  
Author(s):  
Khalida Aissani ◽  
Mouffak Benchohra ◽  
Mohamed Abdalla Darwish
Keyword(s):  
Banach Spaces ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Nonlinear Alternative

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional order integro-differential inclusions with infinite delay in Banach spaces. Sufficient conditions for the existence of solutions are derived by using a nonlinear alternative of Leray–Schauder type for multivalued maps due to Martelli. An example is given to illustrate the theory.

Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions

2018 ◽  
Vol 21 (6) ◽  
pp. 1439-1470 ◽  
Author(s):  
Xiuwen Li ◽  
Yunxiang Li ◽  
Zhenhai Liu ◽  
Jing Li
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Mild Solutions ◽  
Control Problems ◽  
Initial Condition ◽  
Evolution Inclusions ◽  
Technical Details

Abstract In this paper, a sensitivity analysis of optimal control problem for a class of systems described by nonlinear fractional evolution inclusions (NFEIs, for short) on Banach spaces is investigated. Firstly, the nonemptiness as well as the compactness of the mild solutions set S(ζ) (ζ being the initial condition) for the NFEIs are obtained, and we also present an extension Filippov’s theorem and whose proof differs from previous work only in some technical details. Finally, the optimal control problems described by NFEIs depending on the initial condition ζ and the parameter η are considered and the sensitivity properties of the optimal control problem are also established.

scholarly journals Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Jaydev Dabas ◽  
Archana Chauhan ◽  
Mukesh Kumar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Order ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Fractional Equations ◽  
Evolution Differential Equation

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.

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.

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