scholarly journals Mild solutions to nonlocal impulsive differential inclusions governed by a noncompact semigroup

2017 ◽  
Vol 10 (02) ◽  
pp. 492-503
Author(s):  
Shaochun Ji
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Impulsive Differential Inclusions

scholarly journals Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Control Systems ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Fractional Differential

We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce thePC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.

scholarly journals New Study of the Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions with a Sectorial Operator

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 491
Author(s):  
Nawal Alsarori ◽  
Kirtiwant Ghadle ◽  
Salvatore Sessa ◽  
Hayel Saleh ◽  
Sami Alabiad
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Sectorial Operator ◽  
Impulsive Differential Inclusions ◽  
Finite Dimensional ◽  
Generic Class ◽  
The Fixed Point Theorem ◽  
Definition Of ◽  
Theoretical Results ◽  
Contraction Maps

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and the fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of our theoretical results.

scholarly journals Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim
Keyword(s):  
Banach Spaces ◽  
Caputo Derivative ◽  
Infinitesimal Generator ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Compactness Property ◽  
Impulsive Differential Inclusions

We firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions. Secondly, we establish two cases of sufficient conditions for the controllability of the considered control problems.

scholarly journals New Study of Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions With Sectorial Operator

2021 ◽  
Author(s):  
Salvatore Sessa ◽  
Nawal Alsarori ◽  
Kirtiwant Ghadle ◽  
Hayel Saleh
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Multivalued Function ◽  
Sectorial Operator ◽  
Impulsive Differential Inclusions ◽  
Finite Dimensional ◽  
Generic Class ◽  
Definition Of ◽  
Theoretical Results ◽  
Contraction Maps

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

Nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and of order α ∈ (1, 2)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim ◽  
Donal O’Regan ◽  
Adel A. Elmandouh
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Multivalued Function ◽  
Linear Operators ◽  
Solution Set ◽  
Cosine Family ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Noninstantaneous Impulses

AbstractIn this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

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.

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