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 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.

scholarly journals Anti-periodic problem for semilinear differential inclusions involving Hille-Yosida operators

2021 ◽  
pp. 1-31
Author(s):  
Nguyen Thi Van Anh ◽  
Tran Dinh Ke ◽  
Do Lan
Keyword(s):  
Periodic Solutions ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Periodic Problem ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Multivalued Maps ◽  
Integrated Semigroups ◽  
Long Time ◽  
Theoretical Results

In this paper we are interested in the anti-periodic problem governed by a class of semilinear differential inclusions with linear parts generating integrated semigroups. By adopting the Lyapunov-Perron method and the fixed point argument for multivalued maps, we prove the existence of anti-periodic solutions. Furthermore, we study the long-time behavior of mild solutions in connection with anti-periodic solutions. Consequently, as the nonlinearity is of single-valued, we obtain the exponential stability of anti-periodic solutions. An application of theoretical results to a class of partial differential equations will be given.

scholarly journals On generalized boundary value problems for a class of fractional differential inclusions

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Irene Benedetti ◽  
Valeri Obukhovskii ◽  
Valentina Taddei
Keyword(s):  
Differential Inclusions ◽  
Nonlinear Term ◽  
Reflexive Banach Space ◽  
Mild Solutions ◽  
Linear Part ◽  
Fractional Differential Inclusions ◽  
Local Conditions ◽  
Non Local ◽  
Fractional Differential ◽  
Theoretical Results

AbstractWe prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-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 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 Solvability for a Class of Integro-Differential Inclusions Subject to Impulses on the Half-Line

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 224
Author(s):  
Paola Rubbioni
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Distributed Delay ◽  
Half Line ◽  
Fading Memory ◽  
Cauchy Problems ◽  
Definition Of ◽  
External Forces ◽  
With Memory ◽  
Dynamics Process

In this paper, we study a semilinear integro-differential inclusion in Banach spaces, under the action of infinitely many impulses. We provide the existence of mild solutions on a half-line by means of the so-called extension-with-memory technique, which consists of breaking down the problem in an iterate sequence of non-impulsive Cauchy problems, each of them originated by a solution of the previous one. The key that allows us to employ this method is the definition of suitable auxiliary set-valued functions that imitate the original set-valued nonlinearity at any step of the problem’s iteration. As an example of application, we deduce the controllability of a population dynamics process with distributed delay and impulses. That is, we ensure the existence of a pair trajectory-control, meaning a possible evolution of a population and of a feedback control for a system that undergoes sudden changes caused by external forces and depends on its past with fading memory.

scholarly journals Existence of Solutions for Fractional-Order Neutral Differential Inclusions with Impulsive and Nonlocal Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Chao Song ◽  
Tao Zhu ◽  
Jinde Cao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Maps ◽  
Impulsive Differential Inclusions ◽  
Theoretical Results

This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example is given to show the effectiveness of theoretical results.

scholarly journals Global Attractor for Second-Order Nonlinear Evolution Differential Inclusions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Guangwang Su ◽  
Funing Lin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Attractor ◽  
Differential Inclusions ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Nonlinear Evolution ◽  
Mild Solutions ◽  
Second Order ◽  
The Fixed Point Theorem

In this paper, we address the model of global attractor formulated in the form of evolution differential inclusions with second order in Banach spaces. Firstly, based on the fixed point theorem, the existence result of mild solutions is deduced. Then, by implementing the measure of noncompactness, the existence of global attractor associated with m -semiflow is validated. Finally, a concrete application of the main result is demonstrated to enhance the practical signification.

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.

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