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 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 results for fractional integro-differential inclusions with state-dependent delay

2017 ◽  
Vol 4 (1) ◽  
pp. 62-77
Author(s):  
Giovana Siracusa ◽  
Hernán R. Henríquez ◽  
Claudio Cuevas
Keyword(s):  
Differential Inclusions ◽  
Mild Solutions ◽  
Existence Results ◽  
Materials With Memory ◽  
State Dependent ◽  
State Dependent Delay ◽  
Contractive Maps ◽  
Infinite State ◽  
With Memory ◽  
Condensing Maps

AbstractIn this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

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.

Organizing for Influence: The Relationship of Structure to Impact

1987 ◽  
Vol 6 (2) ◽  
pp. 105-116
Author(s):  
Sheila M. Neysmith
Keyword(s):  
Participant Observation ◽  
Organizational Structures ◽  
Allocation Policy ◽  
Composition And Structure ◽  
Policy Statements ◽  
Group Members ◽  
Definition Of ◽  
External Forces ◽  
Political Economic ◽  
Relationship Of

ABSTRACTThis case study is an analysis of a mandated municipal senior's group. Earlier work has suggested that variability in effectiveness is related to organizational structures, external forces and the level of institutional change sought.In this study information was obtained on the political, economic and social context within which the group operated; its organizational composition and structure; its objectives and strategies employed to achieve these; and resources available to the group. Outcome was assessed in terms of impact on programs, resource allocation, policy statements, changes in the definition of issues, and influence on decision makers. Data collection methods included non-participant observation; taped interviews with group members and leaders; key informants in the community; and content analysis of written committee documents.

scholarly journals Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 630
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Nonlinear Alternative ◽  
Contractive Map ◽  
Fractional Differential ◽  
Definition Of

In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results.

scholarly journals Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Rodrigo Ponce
Keyword(s):  
Banach Spaces ◽  
Fractional Derivatives ◽  
Mild Solutions ◽  
Cauchy Problems ◽  
Families Of Operators ◽  
Resolvent Families

We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases0<α<1and1<α<2.

scholarly journals Ultrafast epithelial contractions provide insights into contraction speed limits and tissue integrity

2018 ◽  
Vol 115 (44) ◽  
pp. E10333-E10341 ◽  
Author(s):  
Shahaf Armon ◽  
Matthew Storm Bull ◽  
Andres Aranda-Diaz ◽  
Manu Prakash
Keyword(s):  
Apical Cell ◽  
Physiological Role ◽  
Marine Animal ◽  
Trichoplax Adhaerens ◽  
Contraction Speed ◽  
Order Of Magnitude ◽  
Tissue Rupture ◽  
Epithelial Layers ◽  
Definition Of ◽  
External Forces

By definition of multicellularity, all animals need to keep their cells attached and intact, despite internal and external forces. Cohesion between epithelial cells provides this key feature. To better understand fundamental limits of this cohesion, we study the epithelium mechanics of an ultrathin (∼25 μm) primitive marine animal Trichoplax adhaerens, composed essentially of two flat epithelial layers. With no known extracellular matrix and no nerves or muscles, T. adhaerens has been claimed to be the “simplest known living animal,” yet is still capable of coordinated locomotion and behavior. Here we report the discovery of the fastest epithelial cellular contractions known in any metazoan, to be found in T. adhaerens dorsal epithelium (50% shrinkage of apical cell area within one second, at least an order of magnitude faster than other known examples). Live imaging reveals emergent contractile patterns that are mostly sporadic single-cell events, but also include propagating contraction waves across the tissue. We show that cell contraction speed can be explained by current models of nonmuscle actin–myosin bundles without load, while the tissue architecture and unique mechanical properties are softening the tissue, minimizing the load on a contracting cell. We propose a hypothesis, in which the physiological role of the contraction dynamics is to resist external stresses while avoiding tissue rupture (“active cohesion”), a concept that can be further applied to engineering of active materials.

scholarly journals Utjecaj interpretacija pojma periferijske umjetnosti Ljube Karamana i Miroslava Krleže na dalmatinsku povijesti umjetnosti

2021 ◽  
pp. 498-510
Author(s):  
Ivana Prijatelj Pavičić
Keyword(s):  
Interwar Period ◽  
Art History ◽  
Central European ◽  
Cultural Paradigm ◽  
Miroslav Krleza ◽  
History Of ◽  
Artistic Styles ◽  
Definition Of ◽  
True Center ◽  
External Forces

Although the so-called „Vienna school“ practised an universalist approach to history of arts, their prominent acters like Alois Riegel and Max Dvořák influenced the nationalist ideas among the Central European art historians in the interwar period. An evident example of such an influence is Croatian art historian Ljubo Karaman (1886‒1971) ‒ a Vienna student who studied the art relations between center and periphery from early 1930s on. His thoughts on this topic were collected in his 1963 book Problemi periferijske umjetnosti. O djelovanju domaće sredine u umjetnosti hrvatskih krajeva (Problems of Peripheral Art. On Influence of Local Surrounding on the Art of the Croatian Areas). Colonial character of the Karaman’s definition of the center/periphery relation is clear in his notion that the dissemination and assimilation of the artistic styles is always one-way: from developed center to the province. His definition of „peripheral art“ appeared as a reaction to the works of famous „Vienna school“ scholars from early 20th century (particularly Polish-Austrian art historian Strzygowski). It is based on the idea of external, political and artistic influences in Dalmatia as external forces of artistic exchange. A prominent writer and encyclopaedist Miroslav Krleža turned upside-down the idea of the artistic transfer from the advanced West toward underdeveloped East/Balkans as a periphery at the edge of civilisation. In his discussion on the Second Congress of writers in Zagreb he promoted the idea of the periphery as a true center. During 1950s, Krleža strongly influenced the formation of a new cultural paradigm, and forging of the new scientific paradigm within art history in Croatia. In her paper, the author explores how texts of the Croatian art-history scholars regarding ancient Dalmatian art were influenced by Karaman’s and Krleža’s ideas and concepts on peripheral, provincial, and border-line art.

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